Stats
The probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In 9 traffic fatalities, find the probability that the #, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is: A. exactly 3; at least 3; at most 3 B. between 2-4, inclusive C. Find the mean of the random variable Y. D. Interpret the mean. a. On average, of this many traffic fatalities, 1 will involve an intoxicated or alcohol-impaired driver or nonoccupant. b. In every 9 traffic fatalities, exactly this many will involve an intoxicated or alcohol-impaired driver or nonoccupant. c. On average, of 9 traffic fatalities, this many will involve an intoxicated or alcohol-impaired driver or nonoccupant. E. Obtain the standard deviation of Y.
"Success" = fatality, p=0.4, n=9 Binomial Probability Formula: p(Y=y) = [n!/(y!(n-y)!)] • p^y • (1-p)^n-y Aa. Exactly 3: p(Y=3) = 0.2508 BPF: p(Y=3) = 9!/[3!(9-3)!] • (0.4^3) • (0.6^6) Ab. At least 3: = 0.7682 Find ∑p(Y=0,1,2) and subtract from 1 Ac. At most 3: p(Y=0,1,2,3) = 0,4826 B. p(Y=2-4) = 0.6629 Find ∑p(Y=2,3,4) C. µ = 3.6 µ of BRV = (n # of trials)(p) = (9)(0.4) D. c. On average, of 9 traffic fatalities, this many will involve an intoxicated or alcohol-impaired driver or nonoccupant. E. σ =1.47 Standard Deviation of Binomial Random Variable: σ = √{n • p • (1-p)} σ = √{9 • 0.4 • 0.6}
For the month of February in a certain city, 38% of the days are cloudy. Also in the month of February in the same city, 34% of the days are cloudy and snowy. What's the probability that a randomly selected day in February will be snowy if it's cloudy?
0.895 -- (34/100) / (38/100) = 17/19
Suppose 8 cars start at a car race. In how many ways can the top 3 cars finish the race?
336 Permutations rule (order matters!) ₈P₃ = 8!/(8-3)!
The exam scores for students in an intro stats class are: 77, 33, 34, 40, 49 91, 38, 43, 67, 39 69, 53, 100, 87, 56 84, 34, 74, 97, 69 51, 69, 69, 61, 58 A. Complete the frequency distribution. Score | Freq. 30-39 40-49 50-59 60-69 70-79 80-89 90-100 B. Find the width of the classes. Class | Width 30-39 40-49 50-59 60-69 70-79 80-89 90-100 C. Which set of classes is appropriate if you wanted all the classes to have the same width? a. 40-49, 50-59, 60-69, 70-79, 80-89, 90-99 b. 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100 c. 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99 d. 41-50, 51-60, 61-70, 71-80, 81-90, 91-100 e. 31-40, 41-50, 51-60, 61-70, 71-80, 81-90, 91-100 f. 30-40, 41-49, 50-59, 60-69, 70-79, 80-89, 90-100
A. 5 3 4 6 2 2 3 B. All are 10, except 90-100 which is 11 C. c. 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99 -- can't be a) wouldn't show any of the scores in the 30's -- can't be b) "double dips" i.e. 30-40 and 40-50 -- can't be c) doesn't go high enough, the 100 score wouldn't show -- can't be d) doesn't go low enough -- can't be f) class widths aren't uniform
Suppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded: 0.19, 0.19, 0.20, 0.19 0.21, 0.21, 0.22, 0.24 0.26, 0.27, 0.29, 0.29 0.30, 0.31, 0.31, 0.31 A. Construct a normal probability plot of the data. B. Use the normal probability plot to ID any outliers. a. The normal probability plot doesn't show any outliers. b. The normal probability plot shows 1 outlier. c. The normal probability plot shows 2 outliers. C. Based on the probability plot, does the sample appear to come from a normally distributed population? a. No, since the relationship b/w the expected z-values and the observed values isn't linear. b. Yes, since the relationship b/w the expected z-values and the observed values isn't linear. c. Yes, since the relationship b/w the expected z-values and the observed values is approximately linear. d. No, since the relationship b/w the expected z-values and the observed values is approximately linear.
A. B. a. The normal probability plot doesn't show any outliers. C. a. No, since the relationship b/w the expected z-values and the observed values isn't linear.
Suppose a sample of the height in inches of players in the starting lineup of a particular basketball team was obtained and shown: 78,66,76,70,74. Use a normal probability plot to assess whether the sample data could have come from a population that's normally distributed. A. Construct a normal probability plot of the data. B. Use the normal probability plot to identify any outliers. a. The normal probability plot shows 1 outlier. b. The normal probability plot shows 2 outliers. c. The normal probability plot shows no outliers. C. Based on the probability plot, does the sample appear to come from a normally distributed population? a. Yes, since the relationship b/w the expected z-values and the observed values is approximately linear. b. Yes, since the relationship b/w the expected z-values and the observed values is not linear. c. No, the relationship b/w the expected z-values and the observed values is approximately linear. d. No, the relationship b/w the expected z-values and the observed values is not linear.
A. B. b. The normal probability plot shows no outliers. Find Q1 and Q3: 68,77 Find IQR: 77-68 = 9 Lower limit: Q1 - 1.5(IQR) = 68 - 1.5(9) = 54.5 Upper limit: Q3 + 1.5(IQR) = 77 + 1.5(9) = 90.5 C. c. No, the relationship b/w the expected z-values and the observed values is approximately linear.
The table provides a freq. dist. for the # rooms in this country's housing units (in thousands). Rooms | # units 1 | 560 2 | 1,452 3 | 10,991 4 | 23,364 5 | 27,912 6 | 24,612 7 | 14,679 8+ | 17,293 A = event that the unit has at most 3 rooms B = event that the unit has at least 4 rooms C = event that the unit has 5-7 rooms, inclusive D = event that the unit has more than 7 rooms A. Among the events A, B, C, and D, identify the collections of events that are mutually exclusive. A&B: A&C: A&D: B&C: B&D: C&D: B. Are each of the following groupings of events mutually exclusive? A,B&C: A,B&D: A,C&D: B,C&D: A,B,C&D:
A. Yes Yes Yes No No Yes B. No No Yes No No
A school district administers a standard test of reading skills. Then the director compares the average score for the district w/ the national average. The graph was presented to the school board in 2005. Vertical axis: 0-20 Horizontal axis: 2000-2005 2000: District 17.5, National 20 2001: D 20, N 20 2002: D 17.5, N 19 2003: D 17.5, N 17.5 2004: D 19, N 19 2005: D 18, N 17.5 A. Obtain a truncated version of the graph so that the bars start at 15. B. What misleading impression about the year 2005 scores is given by the truncated graph? a. The ratio of the district to the national average appears larger than it actually is. b. The difference between the district and national averages appears too small. c. The ratio of the district to the national average appears smaller than it actually is. d. The new graph isn't misleading for the year 2005.
A. a. (graph w/ bigger gap in 2000) B. a. The ratio of the district to the national average appears larger than it actually is.
Define: A. Observational study a. In an observational study, researchers look at all the members of the group being studied. b. In an observational study, researchers impose treatments and controls and then observe characteristics and take measurements. c. In an observational study, researchers simply observe characteristics and take measurements, as in a sample survey. B. Designed experiment a. In a designed experiment, researchers simply observe characteristics and take measurements, as in a sample survey. b. In a designed experiment, researchers look at all the members of the group being studied. c. In a designed experiment, researchers impose treatments and controls and then observe characteristics and take measurements.
A. c. In an observational study, researchers simply observe characteristics and take measurements, as in a sample survey. B. c. In a designed experiment, researchers impose treatments and controls and then observe characteristics and take measurements.
The class levels of the students in a particular class are shown: Fr, So, Fr, Sr, So, Jr, So, Jr Sr, So, Sr, So, Fr, Sr, Fr, Jr Jr, Jr, Sr, Jr, Sr, So, Fr, Jr Fr, Fr, Fr, Sr, Fr, Fr, Jr, Jr So, So, Jr, Jr, Sr, Jr, Jr, Sr A. Determine a frequency distribution. Class level | Frequency Fr So Jr Sr B. Obtain a relative-frequency distribution. Class level | Rel. Freq. Fr So Jr Sr C. Draw a pie chart. D. Construct a bar chart.
A. 10 8 13 9 -- Tally up totals B. 0.25 0.2 0.325 0.225 -- Rel. Freq. = Freq/# obs
An insurance company crashed 4 cars of the same model at 5 mph. The costs of repair for each were $413, $439, $453, and $226. A. Find the mean. B. Find the median. C. Find the mode.
A. $382.74 B. $426 C. The mode doesn't exist.
A bag of 31 tulip bulbs contains 13 red tulip bulbs, 9 yellow tulip bulbs, and 9 purple tulip bulbs. A. What's the probability that 2 randomly selected tulip bulbs are both red? B. What's the probability that the 1st bulb selected is red, and the 2nd yellow? C. What's the probability that the 1st bulb selected is yellow, and the 2nd red? D. What's the probability that 1 bulb is red, and the other yellow?
A. 0.168 -- Gen. Mult. Rule: P(A&B) = P(A)•P(B|A) -- = (13/31)(12/30) B. 0.126 -- Gen. Mult. Rule = (13/31)(9/30) C. 0.126 -- Gen. Mult. Rule = (9/31)(13/30) D. 0.252 -- 0.126•2
The table provides a freq. dist. for the # of rooms in this country's housing units. Freq. are in thousands. Rooms | # of units 1 | 550 2 | 1,462 3 | 10,916 4 | 23,334 5 | 27,978 6 | 24,655 7 | 14,655 8+ | 17,296 A housing unit is selected at random. A. Find the probability that the housing unit obtained has 4 rooms. B. Find the probability that the housing unit obtained has more than 4 rooms. C. Find the probability that the housing unit obtained has 1 or 2 rooms. D. Find the probability that the housing unit obtained has fewer than 1 room. E. Find the probability that the housing unit obtained has 1+ rooms.
A. 0.193 -- freq. of having 4 rooms / ∑(all of the frequencies) -- = 23,334/120,846 B. 0.700 -- freq. of having more than 4 rooms / ∑(all of the frequencies) -- = ∑(freq. for 5,6,7,8+ rooms) / ∑(all of the frequencies) = 84,594 / 120,846 C. 0.017 -- ∑(freq. for 1,2 rooms) / ∑(all of the freq.'s) -- = 2012/120,846 D. 0 E. 1
2 cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are black if: A. The 1st card is replaced before the 2nd card is drawn. B. The 1st card isn't replaced before the 2nd card is drawn.
A. 0.25 26/52 • 26/52 B. 0.245 26/52 • 25/51
Assume that the variable under consideration has a density curve. It's given that 26.6% of all possible obs. of the variable are less than 20. A. Determine the area under the density curve that lies to the left of 20. b> Determine the area under the density curve that lies to the right of 20.
A. 0.266 26.6% / 100% B. 0.734 1-0.266
A recent census found that 51.9% of adults are female, 10.7% are divorced, and 5.8% are divorced females. For an adult selected at random, let F be the event that the person is female, and D be the event that the person is divorced. A. Obtain P(F). B. Obtain P(D). C. Obtain P(F&D). D. Determine P(F or D). E. Find the probability that a randomly selected adult is male.
A. 0.519 B. 0.107 C. 0.056 - P(F&D) = P(F)•P(D) = 0.519•0.107 D. 0.57 - P(F or D) = P(F) + P(D) - P(F&D) = 0.519 + 0.107 - 0.056 E. 0.481 P(male) = P(not female) = 1 - P(female) = 1 - 0.519
Assume that women's heights are normally distributed with a mean µ=64.7", and a standard deviation given by σ=1.9". A. If 1 woman is randomly selected, find the probability that her height is less than 65". B. If 41 women were randomly selected, find the probability that they have a mean height less than 65".
A. 0.5636 Want P(X<65) z = (65-64.7)/1.9 = 0.1579 p(z=0.1579) = 0.5636 B. 0.8438 Want P(xbar<65) z = (65-64.7)/(1.9/√41) = 1.01 p(z=1.01) = 0.8438
Determine the area under the standard normal curve that lies between: A. z = -1.48 and 1.48 B. z = -1.93 and 0 C. z = 0.42 and 1.22
A. 0.8612 p(1.48) - p(-1.48) = 0.9306 - 0.0694 B. 0.4732 p(0) - p(-1.93) = 0.5000 - 0.0268 C. 0.226 p(1.22) - p(0.42) = 0.8888 - 0.6628
Find the area of the shaded region for each standard normal curve. A. z1 = -1.62, z2 = 1.83 - shaded region is between the 2 B. z1 = -1.48, z2 = 1.48 - shaded region is to the left of z1, and to the right of z2 C. z1 = -1.68, z2 = 1.68 - shaded region is b/w the 2
A. 0.9138 z1 = 0.0526 z2 = 0.9664 z2 - z1 = 0.9664 - 0.0526 B. 0.1388 z1 = 0.0694 z2 = 0.9306 area to the left of z1 = 0.0694 area to the right of z2 = 1-z2 = 1-0.9306 = 0.0694 0.0694 + 0.0694 = 0.1388 C. 0.9070 z1 = 0.0465 z2 = 0.9535 z2 - z1 = 0.9535 - 0.0465
The following is a probability distribution for the # of Mexican-American jurors, X, on a 12 person jury. The jury was randomly selected from a population in which 80% of the people are Mexican-American. x | P(X=x) 0 | 0 1 | 0 2 | 0 3 | 0 4 | 0.001 5 | 0.003 6 | 0.016 7 | 0.053 8 | 0.133 9 | 0.236 10| 0.283 11| 0.206 12| 0.069 A. Use the special addition rule and the probability distribution to determine P(X≥8). B. Use the special addition rule and the probability distribution to determine P(X=6). C. Use the special addition rule and the probability distribution to determine P(6≤X≤8).
A. 0.927 - ∑P(X=8,9,10,11,12) B. 0.016 C. 0.202 - ∑P(6,7,8)
The standard deviation of the lengths of hospital stay is 8.8 days. A. For the variable "length of hospital stay," determine the sampling distribution of the sample mean for samples of 80 patients. B. Obtain the probability that the sampling error made in estimating the population mean length of stay by the mean length of stay of a sample of 80 patients will be at most 2 days.
A. 0.9839 σ(sub xbar) = σ/√n = 8.8/√80 B. 0.9576 z₁ = 2/0.9839 = 2.03 z₂ = -2/0.9839 = -2.03 p(2.03) = 0.9788 p(-2.03) = 0.0212 0.9788 - 0.0212 = 0.9576
10 cities: Tokyo, San Francisco, Long Beach, Okinawa, Miami, NY, Hong Kong, San Pedro, London, Lyon A. There are 45 possible samples (w/o replacement) of size 2 that can be obtained from these 10 cities. If a simple random sampling procedure is used, what's the chance of selecting HK & NY? B. There are 252 possible samples (w/o replacement) of size 5 that can be obtained from these 10 cities. If a simple random sampling procedure is used, what's the chance of selecting San Fran, London, Long Beach, Tokyo & Lyon?
A. 1/45 B. 1/252
You draw a card at random from a standard deck of 52 cards. Find the following conditional probabilities. A. The card is a spade, given that it's black. B. The card is black, given that it's a spade. C. The card is an 8, given that it's black. D. The card is a king, given that it's a face card.
A. 1/8 26/52 • 13/52 B. 1/8 13/52 • 26/52 C. 2/52 26/52 • 4/52 D. 3/169 12/52 • 4/52
A pediatrician tested the cholesterol levels of several young patients. The rel-freq histogram shows the readings for some patients who had high cholesterol levels. 195-199: 0.1 200-204: 0.1 205-209: 0.15 210-214: 0.3 215-219: 0.25 220-225: 0.1 A. What percentage of patients have cholesterol levels b/w 205 and 209, inclusive? B. What percentage of patients have levels of 215 or higher? C. If the number of patients is 20, how many have levels between 210 and 214, inclusive?
A. 15% B. 35% C. 6
The table displays a freq. distribution for the # of crew members on each shuttle mission over a 10 year period. Let X denote the crew size on a randomly selected shuttle from this time period. Crew size: 2 | 3 | 4 | 5 | 6 Frequency: 3 | 4 |33|18|13 A. What are the possible values of the random variable X? B. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 5. C. Find P(X=3). D. Obtain the probability distribution of X. X | 2 | 3 | 4 | 5 | 6 P(X) | E. Construct a probability histogram for X.
A. 2,3,4,5,6 B. {X=5} C. P(X=3) = 0.056 add up all of the frequencies (71), do 4/71 D. 0.042 0.056 0.465 0.254 0.183 Do same process as above
A hand of 5-card draw poker consists of an unordered arrangement of 5 cards from an ordinary deck of 52 playing cards. A. How many 5 card draw poker hands are possible? B. How many different hands consisting of one 4 and four 2's are possible? C. The hand in part B is an example of a 4 of a kind: 4 cards of 1 denomination and 1 of another. How many different 4 of a kinds are possible? D. Calculate the probability of being dealt a 4 of a kind.
A. 2,598,960 52C5 B. 24 [4C3][4C2] C. 3,744 Pick a card type: 13 ways Pick 3 of the 4 cards: 4C3=4 Pick a 2nd card type: 12 ways Pick 2 of the 4 cards: 4C2= 6 Total = 13*12*4*6 = 3744 full houses possible. D. 0.00144 Calculate the probability of being dealt a full house. 3744/2,598,960
The rel-freq. histogram for the heights of female students: Height | Freq. | Rel. Freq. 60≤61| 3 | 0.0098 61≤62| 9 | 0.0294 62≤63| 26 | 0.0850 63≤64| 70 | 0.2288 64≤65| 88 | 0.2876 65≤66| 72 | 0.2353 66≤67| 29 | 0.0948 67≤68| 7 | 0.0229 68≤69| 2 | 0.0065 Total freq: 306 Total RF: 1 A. The area under the normal curve w/ parameters µ=64.5 and σ=1.9 that lies to the left of 63 is 0.2148. Use this to estimate the percentage of female students who are shorter than 63". B. Use the rel-freq. distribution to obtain the exact percentage of female students who are shorter than 63".
A. 21.48% Given: area to the left of 63" = 0.2148. Do that x100%. B. 12.42% Add up all of the rel. freq.'s through 63".
Each year, a magazine compiles a list of the 400 richest people in a country. As of 2008, the top 10 are: Person | Wealth ($billions) A | 55.6 B | 45.8 C | 38.8 D | 27.1 E | 24.8 F | 24.4 G | 24.4 H | 24.2 I | 19.4 J | 19.4 A. Find the mean. B. Find the median. C. Find the mode. a. The mode is _____ $billion. b. The modes are _____ $billion. c. The data set has no mode.
A. 30.39 B. 24.6 C. b. 24.4, 19.4
The data represents the ages of the winners of an award for the past 5 years: 34,56,25,39,45 A. Determine the population mean age, µ, of the 5 winners. B. Consider samples of size 2 w/o replacement. Find the mean of the variable (x bar). Ages | (x bar) 34,56| 45 34,25| 29.5 34,39| 36.5 34,45| 39.5 56,25| 40.5 56,39| 47.5 56,45| 50.5 25,39| 32 25,45| 35 39,45| 42 C. Find µ(sub x bar), using only the result of part A.
A. 39.8 B. 39.8 C. 39.8
During 1 year, the # of motorcycle accidents in a region were tabulated by day of the week for paved roads and dirt roads and resulted in this data. .............M | T | W | R | F | Sa| Su Paved 87 |106 |82 | 99|102|91| 64 Dirt 80 | 58 | 51| 47 | 57| 95|107 A. The range of paved road accidents is ____. B. The range of dirt road accidents is ___. C. The standard deviation for the # of accidents on paved roads is ___. D. The standard deviation for the # of accidents on dirt roads is ___.
A. 42 -- 106-64 = 42 B. 60 -- 107-47 = 60 C. 14.3 -- Std. Dev. = √{(∑xi - xbar)/(n-1)} -- = √{ [(87-90)² + (106-90)² + (82-90)²...]/(7-1) D. 23.4 -- same formula as C
Assume that the variable under consideration has a density curve. The area under the density curve that lies to the right of 10 is 0.423. A. What percentage of all possible observations of the variable exceed 10? B. What percentage of all possible observations of the variable are at most 10?
A. 42.3% Area given lies to the RIGHT, so it's what's GREATER than 10. B. 57.7% 100% - 42.3%
The data represents the ages of the winners of an award for the past 5 years: 54, 43, 32, 34, 51 A. Determine the population mean age, µ, of the 5 winners. B. Consider samples of size 3 w/o replacement. Find the mean of the variable (x bar). Ages | (x bar) 54,43,32| 43.00 54,43,34| 43.67 54,43,51| 49.33 54,32,34| 40.00 54,32,51| 45.67 54,34,51| 46.33 43,32,34| 36.33 43,32,51| 42.67 32,34,51| 39.00 C. Find µ(sub x bar), using only the result of part A.
A. 42.8 B. 42.8 C. 42.8
Assume that adults have IQ scores that are normally distributed with a mean of µ=100 and a standard deviation σ=15. A. Find the percentage of adults that have an IQ 83-117. B. Find the percentage of adults that have an IQ exceeding 119. C. Determine the quartiles for adult IQs. D. Obtain the 95th percentile for the IQ of adults.
A. 74.16% z₁ = (83-100)/15 = -1.13 z₂ = (117-100)/15 = 1.13 p(-1.13) = 0.1292 p(1.13) = 0.8708 0.8708 - 0.1292 = 0.7416 0.7416 • 100% = 74.16% B. 10.20% z = (119-100)/15 = 1.27 p(1.27) = 0.8980 1-0.8980 = 0.1020 0.1020 • 100% = 10.20% C. Q1 = 89.9 Q2 = 100 Q3 = 110.1 z = µ + σ • z Q1: 100 + 15(-0.675) = 89.875 Q2: (is the mean) Q3: 100 + 15(0.675) = 110.125 D. 124.68 p(z<x) = 0.95 Value of z to the cumulative probability of 0.95 from the normal table is 1.64 p(x-µ/σ < x-100/15) = 0.95 That is, (x-100/15) = 1.64 Therefore, x = 1.64 • 15 + 100 = 124.675
For a recent 10k run, the finishers are normally distributed with mean 55 minutes and standard deviation 8 minutes. A. Determine the % of finishers w/ times b/w 45-66 min. B. Find the % of finishers w/ times less than 70 min. C. Obtain the 40th percentile for the finishing times. D. Find the 7th decile for the finishing times.
A. 78.88% z1 = (45-55)/8 = -1.25 p(z1) =0.1056 z2 = (65-55)/8 = 1.25 p(z2) = 0.8944 z2 - z1 = 0.8944 - 0.1056 = 0.7888 0.7888 x 100% = 78.88% B. 96.99% z(70) = (70-55)/8 = 1.875 p(1.88) = 0.9699 x 100% = 96.99% C. 53 P(X≤x) = 0.40 → P(Z≤(x-55)/8) = 0.40 = (x-55)/8 = -0.25 Use algebra to solve for x, x=53 ∴ 40% of runners finish w/ times less than 53 min. D. 59.192 P(X<x) = 0.7 P[(X-µ)/σ < (x-55)/8] = 0.7 P(Z < z) = 0.7 (x-55)/8 = 0.524 P(X≤x) = 0.70 → P(Z≤(x-55)/8) = 0.70 = (x-55)/8 = Use algebra to solve for x, x=
A study finds that the carapace length of an adult spider is normally distributed with a mean of 19.42 mm and a standard deviation of 1.98 mm. Let x denote carapace length for the adult spider. A. Sketch the distribution of the variable x. B. Obtain the standardized version, z, of x. a. z = (x-1.98)/19.42 b. x = (z-19.42)/1.98 c. x = (z-1.98)/19.42 d. z = (x-19.42)/1.98 C. Identify and sketch the distribution of z. D. Find the z-scores that correspond to the percentage of adult spiders that have carapace lengths between 17-18mm. E. Find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 20mm: lies to the RIGHT of _____.
A. Has mean in middle B. d. z = (x-19.42)/1.98 C. has 0 in middle D. 11.12% and 23.58% z1 = (17-19.42)/1.98 = -1.22 p(-1.22) = 0.1112 x 100% = 11.12% z2 = (18-19.42)/1.98 = -0.72 p(-0.72) = 0.2358 x 100% = 23.58% E. 38.59% z = (20-19.42)/1.98 = 0.2929 p(0.29) = 0.6141 1 - 0.6141 = 0.3859 x 100% = 38.59%
5 state officials are listed: Lieutenant Governor (L), Secretary of State (S), Attorney General (A), Representative (R), and Press Secretary (P). A. List all 10 possible samples (w/o replacement) of size 3. B. If a simple random sampling procedure is used to obtain a sample of 3 officials, what are the chances that it's the 1st sample on your list in part A? The 2nd sample? The 10th sample?t
A. LSA, LSR, LSP, LAR, LAP, LRP, SAR, SAP, SRP, ARP B. 0.1 0.1 0.
The data represent the # of live multiple-delivery births (3+ babies) in a particular year for women 15-54 years old. Age | # Mult. Births 15-19 | 96 20-24 | 513 25-29 | 1632 30-34 | 2821 35-39 | 1845 40-44 | 377 45-54 | 118 A. Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother 30-39 years old. B. Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother who was not 30-39 years old. C. Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother less than 45 years old. D. Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother who was at least 20 years old.
A. P(30-39) = 0.630 -- ∑(freq. of 30-39) / ∑(all freq.) -- = 4,666/7,402 B. P(not 30-39) = 0.370 -- = 1- [P(30-39) -- = 1 - 0.630 C. 0.984 -- P(45-54) = 118/7204 = 0.016 -- 1 - 0.016 = 0.984 D. 0.987 -- P(15-19) = 96/7402 = 0.013 -- 1 - 0.013
A pro hockey player played 20 seasons. The table shows the # of games in which he played during each of his 20 seasons: 35, 81, 69, 71, 74 77, 43, 73, 66, 64, 79, 78, 64, 78, 65, 75, 73, 78, 67, 82 A. Obtain the quartiles. B. Interpret the quartiles. a. The quartiles suggest that 25% of the seasons have less than 65.5 games played, 25% are between 65.5-73, 25% are between 73-78, and 25% are 78+. b. The quartiles suggest that 33% of the seasons have less than 65.5, 33% are b/w 65.5-78, and 33% are 78+. c. The quartiles suggest that all the seasons fall b/w 65.5-78. d. The quartiles suggest that the average of the games played each season is 73. C. Determine the IQR. D. Interpret the IQR. a. The average of Q1 and Q3 is 12.5 b. The approximate difference b/w each quartile is 12.5 c. The data span roughly 12.5 games played. d. The # of games played in the middle 50% of the seasons span roughly 12.5 games. E. Find the 5# summary. F. Interpret the 5# summary. a. The 1st quarter has the greatest variation. The middle 50% has the next largest, the last has the least. b. The 1st quarter has the most seasons recorded. The last has the least. c. The middle 50% has the greatest variation in the data set. The 1st and 4th have the least. d. There aren't as many seasons in the 4th quarter as there are in the 1st. G. Identify any potential outliers, if any. H. Construct and interpret a boxplot. a. The 2 potential outliers are relatively close to the other data points. Most seasons fall w/i the 1st quarter, b/w 60.5-73. b. The 2 potential outlying seasons fall far from the rest of the data. The other seasons vary 64-82. The majority of the seasons had b/w 65.5-78 games played. c. The 2 potential outliers fall far from the rest of the data. The other seasons vary 59-77 games. The majority of seasons had b/w 60.5-73 games played. d. Most seasons had ~73 games played. The highest # of games played was 87, and the lowest was 30.
A. Q1 = 65.5 Q2 = 73 Q3 = 78 B. a. The quartiles suggest that 25% of the seasons have less than 65.5 games played, 25% are between 65.5-73, 25% are between 73-78, and 25% are 78+. C. 12.5 D. d. The # of games played in the middle 50% of the seasons span roughly 12.5 games. E. 35, 65.5, 73, 78, 82 F. a. The 1st quarter has the greatest variation. The middle 50% has the next largest, the last has the least. G. 35, 43 H. b. The 2 potential outlying seasons fall far from the rest of the data. The other seasons vary 64-82. The majority of the seasons had b/w 65.5-78 games played.
An article by a researcher reported on a long-term study of the effects of hurricanes on tropical streams in forests. The study shows that 1 particular hurricane had a significant impact on stream water chemistry. The table shows a sample of 10 ammonia fluxes in the 1st year after the hurricane. Data are in kg/hectare/yr: 77, 127, 61, 130, 165, 163, 158, 77, 93, 130. A. Obtain the quartiles. Q1 = Q2 = Q3 = B. Interpret the quartiles. a. The quartiles suggest that the avg. sample contains 128.5 units. b. The quartiles suggest that 25% of the samples contain less than 77 units, 25% contain between 77-128.5 units, 25% contain between 128.5-158 units and 25% contain greater than 158 units. c. The quartiles suggest that 33% of the samples contain less than 77 units, 33% contain between 77-158 units, and 33% contain greater than 158 units. d. The quartiles suggest that all the samples contain between 77-158 units. C. Determine the IQR. D. Interpret the IQR. a. The # of units contained in the middle 50% of the samples spans roughly 81 units. b. The data span roughly 81 units. c. The approximate difference between each quartile is 81. d. The average of the 1st quartile and the 3rd quartile is 81. E. Find the 5-number summary. F. Interpret the 5-number summary. a. The middle 50% has the least variation. The 1st and 4th quarters have the greatest. b. The 1st quarter has the most samples recorded. The last has the least amount of samples recorded. c. The middle 50% has the greatest variation. The 1st quarter has the next largest variation, and the last quarter has the least variation. d. There aren't as many samples in the 4th quarter as there are in the 1st quarter. G. Identify potential outliers, if any. a. The potential outlier(s) is(are) ___. b. There are no potential outliers. H. Construct and interpret a boxplot. a. The samples range from 61-165 units each. The majority of the samples contain 77-158 units. b. The samples vary from 54.9-148.5 units. The majority of the samples had 69.3-142.2 units. c. Most samples had ~77 units. The highest # of units sampled was 175, and the lowest was 51. d. Most samples fall w/i the 1st quarter of the boxplot, between 72-128.5.
A. Q1 = 77 Q2 = 128.5 Q3 = 158 -- Q2 = median of entire set -- Q1 = median of lower half of set -- Q3 = median of upper half of set B. b. The quartiles suggest that 25% of the samples contain less than 77 units, 25% contain between 77-128.5 units, 25% contain between 128.5-158 units and 25% contain greater than 158 units. C. 81 -- IQR = Q3 - Q1 D. a. The # of units contained in the middle 50% of the samples spans roughly 81 units. E. 61, 77, 128.5, 158, 165 -- 5# summary = Min, Q1, Q2, Q3, Max F. c. The middle 50% has the greatest variation. The 1st quarter has the next largest variation, and the last quarter has the least variation. G. b. There are no potential outliers. -- Lower limit outliers = Q1 - 1.5(IQR) = 77 - 1.5(81) = -44.5 -- Upper limit outliers = Q3 + 1.5(IQR) = 158 + 1.5(81) = 279.5 H. a. The samples range from 61-165 units each. The majority of the samples contain 77-158 units.
According to a technology company, the top 5 countries by avg cable TV cost in a certain area, as of a certain date, are as shown: Rank | Country | Cost ($/month) 1 | A | 53.18 2 | B | 49.85 3 | C | 40.48 4 | D | 38.76 5 | E | 35.52 Identify the type of data provided by the info in each column of the table. Rank: a. Qualitative b. Quantitative, continuous c. Quantitative, discrete Country: a. Qualitative b. Quantitative, continuous c. Quantitative, discrete Cost: a. Qualitative b. Quantitative, continuous c. Quantitative, discrete
A. Quantitative, discrete B. Qualitative C. Quantitative, continuous
Each year, tornadoes that touch down are recorded. The table gives the # of tornadoes that touched down during each month of 1 year. A. Find the range.
A. Range = 199 B. s = 53.31
According to a tech company, the top 5 countries by average Wi-Fi speed in a certain area, as of a certain date, are as shown. Identify the type of data provided by the info in each column. Rank | Country | Speed 1 | A | 67.48 2 | B | 52.93 3 | C | 51.16 4 | D | 48.87 5 | E | 45.61 Rank: a. Quantitative, Discrete b. Qualitative c. Quantitative, Continuous Country: a. Quantitative, Discrete b. Qualitative c. Quantitative, Continuous Speed: a. Quantitative, Discrete b. Qualitative c. Quantitative, Continuous
A. a. Quantitative, Discrete B. b. Qualitative C. a. Quantitative, Discrete
A. In a designed experiment, what are the experimental units? a. The individuals or items on which the experiment's performed. b. The group receiving placebo. c. The group receiving the specified treatment. d. The experimental conditions. B. If the experimental units are humans, what term is often used in place of experimental units? a. Subject b. Placebo c. Treatment d. Factor
A. a. The individuals or items on which the experiment's performed. B. a. Subject
A sample of 50 Anacapa pelican eggs were collected and the concentration of a pollutant, in ppm, was measured. The rel-freq. histogram is shown. A. What's the overall shape of the given distribution? a. triangular b. bell shaped c. bimodal d. right skewed B. Which of the following best describes the given distribution? a. right skewed b. nearly symmetric c. left skewed
A. bell shaped B. nearly symmetric
According to an article, 34% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly selected adults, find the probability that the number, X, who have experienced a breakup at least once during the last 10 years is: A. exactly 5; at most 5; at least 5 B. at least 1; at most 1 C. Between 4-6, inclusive D. Determine the probability distribution of the random variable X. Complete the table: x | P(X=x) 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
A. exactly 5: P(X=5) = 0.1086 at most 5: P(X=0,1,2,3,4,5) = 0.9296 at least 5: P(X=5,6,7,8,9) = 0.1553 B. at least 1: P(X=1,2,3,4,5,6,7,8,9) = 0.9762 at most 1: P(X=0,1) = 0.1339 C. between 4-6, inclusive: P(4≤X≤6) =0.3568 D. P(X=0) = 0.02376268 P(X=1) = 0.11017243 P(X=2) = 0.22702197 P(X=3) = 0.27288499 P(X=4) = 0.21086568 P(X=5) = 0.10862777 P(X=6) = 0. 03730651 P(X=7) = 0.00823650 P(X=8) = 0.00106076 P(X=9) = 0.00006072
The random variable X is the # of color TV sets owned by a randomly selected household w/ an annual income b/w $15k-$29,999. Its probability distribution is shown: x | P(X=x) 0 | 0.137 1 | 0.322 2 | 0.219 3 | 0.152 4 | 0.170 A. Find the mean of the random variable. B. Interpret the mean of the random variable. a. The observed value of the random variable will be less than the mean of the random variable in most observations. b. The observed value of the random variable will be equal to the mean of the random variable in most observations. c. As the # of observations, n, DEC, the mean of the observations will approach the mean of the random variable. d. As the # of observations, n, INC, the mean of the observations will approach the mean of the random variable. C. Obtain the standard deviation of the random variable: σ = _____. D. Draw a probability histogram for the random variable.
A. µ = 1.896 Mean of Discrete Random Variable: µ = ∑(x•P(X=x)) B. d. As the # of observations, n, INC, the mean of the observations will approach the mean of the random variable. C. 1.300 √{∑[x²•P(x)] - µx²} D.
The data represent the ages of the winners of an award for the past 5 years: 47, 40, 37, 47, 46 A. Find the population mean age of the 5 winners. B. For samples of size 3, construct a table of all possible samples and their sample means. Age | (x bar) 47,40,37 47,40,47 47,40,46 47,37,47 47,37,46 47,47,46 40,37,47 40,37,46 40,47,46 37,47,46 C. Draw a dotplot. D. For a random sample of size 3, what's the chance that the sample mean will equal the population mean?
A. µ = 43.4 B. 41.33 44.67 44.33 43.67 43.33 46.67 41.33 41 44.33 43.33 C. D. 0 E. 0.9
The data represent the ages of the winners of an award for the past 5 years: 43,48,42,39,48 A. Find the population mean age of the 5 winners. B. For samples of size 3, construct a table of all possible samples and their sample means: Age | (x bar) 43,48,42 43,48,39 43,48,48 43,42,39 43,42,48 43,39,48 48,42,39 48,42,48 48,39,48 42,39,48 C. Draw a dotplot for the sampling distribution of the sample mean for samples of size 3. D. For a random sample of size 3, what's the chance that the sample mean will equal the population mean? E. For a random sample of size 3, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be 2 years or less; that is, determine the probability that (x bar) will be w/i 2 years of µ.
A. µ = 44 B. 44.33 43.33 46.33 41.33 44.33 43.33 43 46 45 43 C. D. 0.8
The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown: x | 2 | 3 | 4 | 5 | 6 | 7 | 8 P(X=x) |0.086|0.047|0.088|0.286|0.121|0.309|0.063 A. Find the mean of the random variable. µ = ______ B. Interpret the mean. a. The observed value of the random variable will be less than the mean of the random variable in most observations. b. As the # of obs, n, INC, the mean of the obs. will approach the mean of the random variable. c. The observed value of the random variable will = the mean of the random variable in most obs. d. As the # of obs, n, DEC, the mean of the obs. will approach the mean of the random variable. C. Obtain the standard deviation of the random variable. σ = _____. D. Draw a probability histogram for the random variable.
A. µ = 5.488 Mean of DRV µ = ∑[x•P(x)] = 0.172 + 0.141 + 0.352 + 1.43 + 0.726 + 2.163 + 0.504 B. b. As the # of obs, n, INC, the mean of the obs. will approach the mean of the random variable. C. σ = 1.654 Std. Dev of DRV: √{∑[x²•P(x)] - µ²} D.
A census bureau collects info about the ages of people in a country. A. Identify the variable: a. The age of each person in the country b. The avg. age of people in the country c. The median age of people in the country d. The age of people in different countries Ab. Identify the population: a. All people b. All people living in the country c. All adults living in the country B. A sample of 6 residents yielded the data: 12,7,25,14,9,8 Ba. The mean and median of these data are: (statistics/parameters) Bb. The sample mean is (designated by which variable?) and = _____ Bc. The sample median is (designated by which variable?) and = _____ C. By consulting the most recent census data, we found the mean age and median age of all residents are 35.4 and 35.2 years. Decide whether those descriptive measures are parameters or stats, and use statistical notation to express the results. Ca. The mean & median age of all residents are (parameters/stats) Cb. The population mean is (what variable?) = 35.4 Cc. The population median is (what variable?) = 35.2
Aa. a. The age of each person in the country Ab. b. All people living in the country. Ba. Statistics Bb. (x bar) = 24.5 Bc. M = 24 Ca. Parameters Cb. µ Cc. n
The table provides a freq. dist. for the # of rooms in this country's housing units (in thousands). Rooms | # units 1 | 588 2 | 1,458 3 | 10,925 4 | 23,351 5 | 27,938 6 | 24,600 7 | 14,653 8+ | 17,291 A. Find the probability that the housing unit obtained has 4 rooms. B. Find the probability that the housing unit obtained has more than 4 rooms. C. Find the probability that the housing unit obtained has 1 or 2 rooms. D. Find the probability that the housing unit obtained has fewer than 1 room. E. Find the probability that the housing unit obtained has 1 or more rooms.
[∑ of freq. = 120,804] A. 0.193 B. 0.699 C. 0.017 D. 0 E. 1
Is this study descriptive or inferential? In a statistical magazine, average professional athletes' salaries in 3 sports were compiled and compared for the years 1993 and 2003. Sport | Avg. salary '93 | Avg. salary '03 A | 1,087 | 2,382 B | 1,394 | 3,970 C | 620 | 1,253 a. Descriptive, b/c the stats are a summary of the avg. salaries of professional athletes in 3 sports. b. Inferential, b/c the stats are a summary of the avg. salaries of pro athletes in 3 sports. c. Descriptive, b/c the stats are used to make an estimate of the avg. salaries of all pro athletes. d. Inferential, b/c the stats are used to make an estimate of the avg. salaries of all pro athletes.
a. Descriptive, b/c the stats are a summary of the avg. salaries of professional athletes in 3 sports.
What is a frequency distribution of qualitative data and why is it useful? a. It's a listing of the distinct values and their frequencies. It's useful b/c it provides a table of the values of the observations and how often they occur. b. It's a chart that displays the distinct values of the qualitative data on a horizontal axis and the frequencies of those values on the vertical axis. It's useful b/c it shows the values of the observations and how often they occur graphically. c. It's a disk divided into wedge-shaped pieces proportional to the relative frequencies of the qualitative data. It's useful b/c it shows the values of the observations and how often they occur graphically. d. It's a listing of the distinct values and their relative frequencies. It's useful b/c it provides a table of the values of the observations and relatively how often they occur. It's also useful for comparing 2 data sets.
a. It's a listing of the distinct values and their frequencies. It's useful b/c it provides a table of the values of the observations and how often they occur.
At a college, there are 120 frosh, 90 soph, 110 jr, and 80 sr. A school administrator selects a simple random sample of 12 of the frosh, a simple random sample of 9 of the soph, a simple random sample of 11 of the jr, and a simple random sample of 8 of the sr. She then interviews all the students selected. Identify the type of sampling used in this example. a. simple random sampling b. stratified sampling c. cluster sampling d. systematic random sampling
b. stratified sampling
Describe if the events are mutually exclusive: Event A: Randomly selecting someone who smokes cigars. Event B: Randomly selecting a male. a. No, b/c someone who smokes cigars can't be male. b. Yes, b/c someone who smokes cigars can be male. c. No, b/c someone who smokes cigars can be male. d. Yes, b/c someone who smokes cigars can't be male.
c. No, b/c someone who smokes cigars can be male.
Before premiering a blockbuster movie at a theater, test screenings are done beforehand. A small number of selected theaters are chosen geographically throughout the country. Each theater chosen is supposed to be representative of theatergoers in that area. Everyone is interviewed when the movie's over. Identify the type of sampling used in this example. a. Stratified sampling b. Systematic sampling c. Attempted census d. Cluster sampling
d. Cluster sampling
Data from a sample of citizens of a certain country yielded the following estimates of average TV viewing time per month for all citizens (in hrs & min). Viewing method | May 08 | May 07 | ∆ (%) Watching TV in home | 127:49 | 121:59 | 5 Watching timeshifted TV | 5:50 | 3:57 | 48 Using Internet | 26:01 | 24:31 | 6 Watching vid on Internet | 2:16 | NA | NA Is the study descriptive or inferential? a. Descriptive, b/c the stats are used to describe the sample. b. Descriptive, b/c the stats are used to make an inference about the population. c. Inferential, b/c the stats are used to describe the sample. d. Inferential, b/c the stats are used to make an inference about the pop.
d. Inferential, b/c the stats are used to make an inference about the pop.
Determine whether the given value is a statistic or a parameter: A sample of professors is selected and it's found that 50% own a vehicle. a. Parameter b/c the value is a numerical measurement describing a characteristic of a sample. b. Parameter b/c the value is a numerical measurement describing a characteristic of a population. c. Statistic b/c the value is a numerical measurement describing a characteristic of a population. d. Statistic b/c the value is a numerical measurement describing a characteristic of a sample.
d. Statistic b/c the value is a numerical measurement describing a characteristic of a sample.
