Statistics Do Nows - Mr. Flanders

Suppose you want to predict the value of Fun Boards stock over the next 12 days using the third-row of a random # table. Allow each digit encountered to represent 1 day. If you encounter an even digit, increase the daily stock price by $1, an even digit decrease by $1. If the initial price is $45/share, what is the price after 12 days ?

$43

Construct a Pareto chart with the given data. letter=type, #=frequency A-22, B-17, C-19, D-31, E-30, F-13

(Order bars from largest to smallest as well)

Construct a histogram with the intervals 33-35, 36-38, 39-41, 42-44 for the #s: 43, 44, 4, 39, 34, 44, 35, 36, 35, 41, 40, 41, 44, 35, 36, 37, 43, 34, 34

(no space between bars)

Display the set of data in a histogram. (Age, Frequency) (50-52, 1); (53-55, 4); (56-58, 4); (59-61, 6); (62-64, 8); (65-67, 7)

(no space in between bars)

a) Construct a frequency histogram from the data b) Draw a frequency line (Temp interval F degrees, Frequency) (61-70, 5); (71-80, 5); (81-90, 8); (91-100, 2); (101-110, 8)

(no space in between bars)

Dara collected over a period of years shows that the average daily temp in Honolulu is µ = 84°F with standard deviation σ = 9°F. Convert the following interval to °F to an interval of z values 66°F < x < 97°F

-2 < z < 1.44

Data collected over a period of years shows that the average daily temperature in Honolulu is µ = 84°F with standard deviation σ = 9°F. Convert the following interval to °F to an interval of z values. 66°F < x < 97°F

-2 ≤ z ≤ 1.4

A bag has 6 marbles: 4 black and 2 white. Draw a tree diagram showing the possible outcomes if a marble is drawn out of the bag and set aside twice.

...

Construct a dotplot of the cost-per-gram data: 1.8, 5.8, 1.5, 3.1, 2.7, 3.1, 2.3, 2.1, 3.3, 2.9, 5.0, 2.5, 5.2, 6.9, 3.6, 5.2, 5.7, 1.8, 5.3

...

Find the class width for 4 classes. Make a frequency table showing class limits, boundaries, midpoints, frequency, and relative frequency. Draw a histogram from the given data: 60, 22, 72, 36, 25, 16, 70, 26, 16, 59, 21, 64, 24, 16, 48, 60, 38, 54, 48, 42

...

Find the class width, the boundaries, midpoints, frequency, relative frequency, and create a histogram of the relative frequencies from these numbers: 68, 95, 102, 70, 60, 70, 80, 87, 69, 74, 86, 71, 101, 85, 46, 70, 83, 18, 73, 37, 58, 85, 86, 92, 90, 82, 62, 77, 86, 75, 100, 88, 71, 63, 90

...

Make a scatter plot of the speed vs. the mpg (Speed, MPG): (20, 24); (30, 28); (40, 30); (50, 28); (60, 24)

...

A biologist is studying a new hybrid tomato. It is known that the seeds of this tomato have probability .48 of germinating. The biologist plants ten seeds. What is the probability that at least 8 seeds will germinate? round to three decimal places

.042

Find the numerical difference between 2 standard deviations and explain why the value is what it is Set A: {2, 5, 12, 7, 23} Set B: {7, 9, 25, 4, 14}

0. The data points vary the same amount around their respective means

Find the area between z = 1.63 and z = 1.94 (Four decimal places)

0.0254

52% of Internet users are somewhat concerned about the confidentiality of their email. Based on this info, what is the probability that for a random sample of 11 Internet users, 6 are concerned about the privacy of their email? (Round to third decimal place)

0.233

Sociologists say that 45% of married woman claim that the husband's mother is the biggest bone of contention in the marriages. Suppose that five married women are having coffee together one morning. Using a table, what is the probability that at least three of them dislike their mother-in-law? (Three decimal places)

0.407

The playing life of a Sunshine radio is normally distributed with mean µ = 154 and standard deviation σ = 183. What is the probability that a radio selected at random will last from 154 to 703 hours?

0.4985

The playing life of a Sunshine radio is normally distributed with mean µ = 154 hours and standard deviation σ= 183. What is the probability that a radio selected at random will last from a 154 to 703 hours?

0.4985

The restaurant has been grossing over $2644 for about 30% of its business days. Find the probability that the restaurant will gross over $2644 fewer than 3 days over the next 5 business days. Round to the third decimal place.

0.837

John is looking to get onto his school hockey team. There are only two positions left on the team and 6 people eligible to fill the spots, including John. If two players from the six are chosen randomly, what are the chances that John will be selected for the team?

1 out 3 chance

Among 350 randomly selected drivers in the 16-18 age bracket, 242 were in a car crash last year. 1) If a driver in that age bracket is randomly selected what is the approximate probability that he or she will be in a car crash during the next year? 2) Is it unusual for a driver in that age bracket to be involved in a car crash during a year? 3) Is the resulting value high enough to be of concern to those in the 16-18 age bracket? Consider an event to be "unusual" if its probability is less than or equal to 0.05. 4) The probability that a randomly selected person in the 16-18 age bracket will be in a car crash this year is approximately_____?

1) 69% 2) no 3) It would be unusual if only about 1-10% had a chance of getting in a car accident and a lot of people get in a car accident. Matter of concern 4) 69%

Find a positive z value x such that 88.36% of the area under the standard normal curve is between -z and z. Use a table

1.57

A family that is known to have two children selected at random from amongst all families with two children, Find the probability that both children are boys given that there is a boy in this family.

1/2 or 1/3 (depending on your philosophy)

Imagine that you have two fair dice labeled 1-8. When rolling the dice, what is the probability that the results of the dice will match?

1/8

Archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in a pueblo. Wood from several excavations gave a mean of (year) 1091 with a standard deviation of 22 years. The distribution of dates was more or less mound shaped and symmetrical about the mean. Use empirical rule to estimate the range of years centered about the mean in which about 95% of the data will be found.

1047 to 1135

What is the sample standard deviation of the data set? 1 - 2, 3 2 - 3, 5, 6, 9, 9 3 - 1, 7, 8 4 - 5 - 1, 2

12.5806

A random sample of battery packages is taken from a population of 50 to check for quality. What would be the 7th battery package for the sample based on these random numbers: 34462 21461 65329

16

Let x have a normal distribution with µ = 49 and σ = 6. Find the probability that an x value selected at random from this distribution is between 51 and 54. In symbols, find P(51 ≤ x ≤ 54). Use a table. Round to four decimal places.

16.74%

What are the stems for the data set 54, 43, 58, 25, 67, 36, 61?

2, 3, 4, 5, 6

Identify the class width used in the frequency distribution (Class Limit, Frequency): (50-52, 5); (53-55, 8); (56-58, 12); (59-61, 13); (62-64, 11)

3

In a sample of 100 color candies, there are 15 red candies, 3 blue, 20 yellow, and 62 brown. Estimate the probability that when a candy is randomly selected, it is one that is blue

3/100 or .03

For the past 15 days, the housekeeping unit has reported the number of rooms not ready by 3:30pm. The director of housekeeping is aware that the distribution is symmetrical bell shaped. It is approximately normal with mean µ = 25.5 and standard deviation σ = 2.5. If housekeeping needed to make a control chart for the reported data, what would be the highest control unit?

33

Assuming that the heights of college women are normally distributed with a mean of 61.7 in and standard deviation of 3.2 in, what is the percentage that are between 61.7 in and 64.9 in?

34%

The playing life of a Sunshine radio is normally distributed with mean µ = 865 hours and standard deviation σ = 163. What is the probability that a radio selected at random will last from 885-1028 hours?

34%

Yvette made the following stem and leaf diagrams of high & low temps for 10 days. How much greater was the highest temp than the lowest temp? Lows_ Stem_ Highs 5332__ 3____ 66 920___4____ 66 259___ 5___ 1259 _____ 6____ 3447

35

A die is labeled 1-6 and rolled 50 times. What is the mean of the outcome of the data below? (Number, Frequency): (1, 4); (2, 3); (3, 6); (4, 10); (5, 14); (6, 13)

4.32 or 4

A single die is labeled 1 to 6 and rolled 50 times. What is the mean outcome of the data? (Number, Frequency): (1, 4); (2, 3); (3, 6); (4, 10); (5, 14); (6, 13)

4.32 or 4

According to Chebyshev's theorem, if x=200 and s=50, what is the interval in which 88.9% of the data should fit

50 to 350

Suppose you score 88% on your midterm and score 72% on your final. Using the weights of 38% for the midterm and 62% for the final exam, find the weighted average of your scores.

78.08%

According to Chebyshev's theorem, what percentage of the data will be within 2.2 standard deviation from the mean? (Round to hundreth place)

79.34%

Below are two sets of #s: {2, 5, 12, 7, 23} and {7, 9, 25, 4, 14}. Find the numerical difference between the two standard deviations if the sets

8.228-8.228 = 0, no difference

Without using a calculator, find the mean and standard deviation of each set. Which data set has the highest standard deviation? A: {9, 10, 11, 7, 13} B: {11, 10, 15, 5, 9} C: {2, 19, 10, 1, 18}

A: mean = 10, standard deviation = 2.2361 B: mean = 10, standard deviation = 3.6056 C: mean = 10, standard deviation = 17.0294 ] biggest S

Define sample space

All the possible outcomes for a problem

Explain extrapolation

Estimating for x-values that are not given in the range

As a procedure is repeated again and again the relative frequency of an event tends to approach the actual probability, this is known as______?

Law of Large Numbers

Without using the calculator find the mean, median , 1st Quartile, 3rd Quartile, and Interquartile Range {9, 24, 18, 21, 12, 6, 15, 27}

Mean = 16.5 1st Q = 10.5 3rd Q = 22.5 IQR = 12

Below are total #points scored by both teams in each game. Display data in a stem and leaf plot and find the median. 45, 46, 59, 53, 47, 37, 52, 39, 23, 66, 39, 41, 30, 50, 51, 37, 69, 69, 27, 47, 43, 61, 21, 44, 75, 45, 31, 47, 44, 31, 22, 54, 56, 46, 38, 56, 55, 31, 50

Median = 45

A test to measure boredom was administered to a group of 4982 adults. The possible scores were 0, 1, 2, 3, and 4, with 4 indicating the highest tolerance for boredom. The test results for the group are shown below: (Score, Number of Subjects) (0, 708); (1, 1732); (2, 1795); (3, 688); (4, 59) What is the possibility that someone in the group who took the test made either a 3 or a 4? (round intermediate steps to two decimal places)

P(3 or 4) = 0.15

The percentage of American men who say they would marry the same woman if they had to do it all over again is 74%. What is the probability that in a group of 9 married men, at least 7 will claim that they would marry the same woman again? (round to three decimal places)

P(r≥7) = 0.573

Find the range, sample mean, sample variance, sample standard deviation, and coefficient of variation {30, 20, 4, 29, 58, 7, 20, 18, 4, 29, 22, 9}

Range = 54, mean = 20.83, Variance = 227.971, standard deviation = 15.0987, CV = 72.48

What does P (A I B) mean?

The probability of event A given event B

What does A^c mean?

The probability that event A will not happen

What does Ā mean?

The probability that event A will not happen

The single trial of some procedure is conducted and the resulting events are analyzed. Describe what it means for two events in a single trial to be disjoint.

The two events cannot happen at the same time if they are disjoint, making them mutually exclusive

A white bin contains 7 blue balls, 4 red balls, and 2 green balls. A black bin contains 3 blue balls, 4 red balls, and 9 green balls. All the balls from both bins are mixed together and then one ball is chosen at random. Are the events "blue ball is chosen" and "ball was from white bin" mutually exclusive? Explain

They are not mutually exclusive because both events can occur simultaneously

A pie chart showing the relative amount of money gathered by different stalls at a fair would show that Games is 90°, Food made $2353, Drinks made $882, and Souvenirs made an unknown amount of money and is an unknown percent. The total amount of money was $5880 a) How much money was collected by the Game stall? b) What percent of the total money was collected by the Souvenir stall? c) What percent of the total money was collected by the Food and Drinks stalls d) What is the ratio of money collected by the Food and Drinks stalls to the money collected by the Game stall?

a) $1470 b) 20% c) 55% d) 11:5

a) Find the highest income b) Find the lowest income c) Find the difference between the highest and lowest scores d) How many employees are earning incomes greater than $350? e) What is the sum of all the incomes between 240 and 500? f) How many employees are earning between $300 and $600? g) If $200 is considered the poverty line, what is the percent of employees who are poor? 1 - 90, 90 2 - 10, 50 3 - 10, 10, 30, 40 , 90, 90 4 - 00, 20, 90 5 - 50, 50, 80 6 - 10, 20

a) $620 b) $190 c) $430 d) 10 employees e) $3630 f) 12 employees g) 11.11%

Explain the mistakes in the statements tomorrow a) My very low correlation of -0.772 shows that there is almost no association between GDP and Infant Mortality Rate b) There was a very strong correlation of 1.22 between Life Expectancy and GDP

a) -0.772 is a strong negative correlation b) Correlation is between -1 and 1. There is no correlation 1.22

A black and a white ball are in a bag together. a) If one ball is drawn out of the bad and then replaced four times in a row, what is the probability of drawing the black ball four times? b) What is the probability of drawing the black ball three times and the white ball once (Not necessarily in that order)?

a) 1/16 b) 1/4

17, 23, 18, 19, 21, 16, 12, 15, 18 a) Find the range b) Find the sample mean c) Find the sample standard deviation

a) 11 b) 17.67 c) 3.24

Below is a list of ages of people who attended a speech a) What is the total number of people younger than 30 who attended the speech? b) What interval of age group (Ex. 1-9) contains the least number of people? c) How many people are between 25 and 40? d) Which stem(s) contains at least 7 people? 1 - 2, 5, 8, 8, 8, 9 2 - 1, 1, 2, 2, 3, 5, 5, 7, 8 3 - 0, 1, 3, 4, 5, 5, 8, 8, 8 4 - 2, 3, 5, 5, 5, 6, 7, 9, 9 5 - 2, 3, 5, 5, 5, 6, 7, 9, 9 6 - 0, 2, 3, 3, 4, 5, 8 7 - 0, 1, 4, 8 8- 1

a) 14 b) 80-89 c) 13 d) 2, 3, 4, 5, and 6

A vending machine automatically pours soft drinks into cups. The amount of soft drinks disposed into a cup is normally distributed with a mean of 7.6 oz and standard deviation of 0.4 oz. a) Examine the probability that the machine will overflow an 8 oz cup b) Examine the probability that the machine will not overflow and 8 oz cup c) The machine has just been loaded with 850 cups. How many of those do you expect will overflow when served?

a) 16% b) 84% c) 136

2, 6, 18, 9, 0, 15, 3, 10 a) Find the range b) Mean c) Sample standard deviation

a) 18 b) 7.875 c) 6.357

In a school, there are 750 students in Year 1. Represented in a pie chart, Year 1 is 150°, Year 2 is 84°, and Year 3 is 126°. a) How many students are in year 2? b) How many students are in year 3? c) What is the total #students in the school? d) What percent of the total #students are in year 3?

a) 420 students b) 630 students c) 1800 students d) 35%

10 students take a test; there were 1000 possible points. Data: 351, 988, 348, 450, 290, 965, 360, 346, 332, 318 a) Compute the mean b) Compute the median and compare it to the mean c) Which average describes most of the students? d) Compute 10% trimmed mean

a) 474.8 b) 349.5, less than the mean c) The median d) 433.75

Male and Blue Eyed = 6; Male and Brown Eyed = 20; Male and Green Eyed = 6; Female and Blue Eyed = 4; Female and Brown Eyed = 16; Female and Green Eyed = 12. 32 Males and 32 Females, 64 people total. a) What % of females are brown eyed? b) What % of brown eyed people are female? c) What % of students are brown eyed females?

a) 50% b) 44.44% c) 25%

Female and Liberal = 35; Female and Moderate = 36; Female and Conservative = 6; Male and Liberal = 50; Male and Moderate = 44; Male and Conservative = 21 a) What percent of the class is male? b) What percent of the class is conservative? c) What percent of the males are also conservative? d) What percent of all students are male and conservative?

a) 59% b) 14% c) 18% d) 10%

a) How many terms have at least 50 members? b) What is the mean team size? Stem-leaves 2 - 2, 4 3 - 4 4 - 0, 6, 9 5 - 4, 6 6 - 3, 9 7 - 7 8 - 5 9 - 0

a) 7 teams b) 55 members

15_ x ___x x 10_ x x ___x x 5__x x x __x x x x x x_ x _0__ 120__ 240 (closets I could get to a graph. Ignore lines) a) Approximately what % of these vineyards are under 60 acres? b) Write a brief description of this distribution

a) >60%, ≈79.36% b) The graph is skewed right

A class of fourth graders takes a diagnostic reading test and the scores are reported by reading grade level. The 5 number summaries for the 14 boys and 11 girls are shown below: Boys: 2.0, 3.9, 4.3, 4.9, 6.0 Girls: 2.8, 3.8, 4.5, 5.2, 5.9 a) Which group has the highest scores? b) Which group has the greatest range? c) Which group has the greater interquartile range? d) Which group's scores appear to be more skewed? Explain e) Which group generally did better on the test? Explain f) If the mean reading level for boys was 4.2 and for girls was 4.6, what is the overall mean for the class?

a) Boys b) Boys c) Girls d) Boys e) Girls f) 4.38

Below is a list of the square foot measurements of offices in a corporation. a) How many offices are exactly 46 square feet? b) How many offices lie between 33 and 57? (Do not include 33 or 57) Stem - leaves 3 - 0, 3, 4, 6, 6, 7, 7, 7, 9, 9 4 - 6, 6, 6, 6, 8 5 - 4, 6 6 - 3, 4, 4, 7, 8, 9, 9

a) Four b) 14

Myra did a study of the number of weeks 10 novels were on a best-seller list. Her data: 7, 15, 48, 2, 12, 20, 10, 15, 102, 24 a) Compute the mean, median, and mode b) Compute a 10% trim mean c) How did the extreme values affect each average

a) Mean = 25.5, Median = 15, Mode = 15 b) Mean = 18.875 c) Pulled the mean up

a) How would you use a random # table to get a random sample of 8 families from a subdivision which contains 92 families? b) Use 66330 33393 95261 95349 to identify the first five families

a) Number the families from 1 to 92. Read consecutive groups of 2 digits until you have twelve distinct numbers from 1 to 92 b) 66, 33, 3, 26, 19

a) Describe how you would use a random # table to get a random sample of 12 shirts from a shipment of 12 b) Use 08811 82711 57392 25252 30333 to identify the first 7

a) Number the shirts 1 to 475. Read consecutive groups of 3 digits until you have 12 distinct #s from 1 to 475 b) 88, 118, 271, 157, 392, 252, 33

a) Describe how to use a random #table to get a random sample of 50 people of a pool of 7,500 people b) Use the line from random #table given below to identify the first 3 people in your sample 94456 48396 73780 06436 86641 69239

a) Randomly choose # from table, record 200 #s moving right then down, creating new #s every 4th digit, discard #s over 7,000 b) 6,483 6,436 1,692

6 people hope to be selected for a game show. 2 of these people are younger than 25 years old. 2 of these six will be chosen at random to be on the show a) What is the sample space for selecting two of these people at random? b) Are the outcomes in the sample space equally likely? c) What is the probability that both chosen are younger than 25? d) What is the probability that both chosen are not younger than 25? e) What is the probability that one is younger than 25 and the other is not?

a) S = ∑ AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF b) Yes c) 0.0667 d) 0.04 e) 0.533

a) Describe how you would use a random number table to get a random sample of 12 men's shirts taken from a shipment of 475 shirts b) Use this line from the ransom number table given below to identify the first seven shirts in your sample 08811, 82711, 57392, 25252, 30333

a) Start from anywhere in a random number table and, in groupings of 3 digits, choose 12 numbers that don't exceed 475 from moving left to right and down the table. b) 88, 118, 271, 157, 392, 252, 033

An insurance company wants to know the proportion of medical doctors in New York to be involved in at least 1 malpractice suit in the last 3 years. They survey a random sample of 200 medical doctors in New York. a) What is the population? b) What is the sample? c) Could the insurance company generalize and say this sample is representative of all medical doctors in the rural areas of the country?

a) The response of all medical doctors in New York b) The response from 200 doctors in the survey c) No. The sample wasn't restricted to medical doctors from rural areas in New York. Many of those in the sample could have come from New York City

A small warehouse employs a supervisor at $1200 a week, an inventory manager at $700 a week, six stock boys at $400 a week, and 4 drivers at $500 a week. a) find the mean and median wage b) how many employees earn more than the mean wage? c) which measure of center best describes a typical wage at this company: the mean or the median? d) which measure of spread would best describe the payroll: the range, the IQR, or the standard deviation and why?

a) mean = 525, median = 450 b) 2 employees c) median b/c of outlier d) IQR

Five balls (2 red, 2 blue, and 1 yellow) are mixed up. At random, one ball is chosen and set aside, and then another ball is chosen and set aside. a) Are these events independent? b) What is the probability that neither ball is blue?b)

a) no b) 0.3 or 30%

Choose the word that does not complete the statement: Statistics is the study of how to ___, ___, ___, and ___ a) randomize. b) analyze. c) collect. d) interpret. e) organize

a) randomize

Tickets numbered 1 to 20 are shuffled and a ticket is drawn at random. a) What is the probability that the ticket drawn has a number which is a multiple of 2 and is also a multiple of 5? b) What is the probability that the ticket drawn has a number which is a multiple of 2 or 5?

a)1/10 or 0.1 b) 12/20 or 0.6

The test scores for the 25 members of the Math class and their relative frequencies are 70-80: 0.08, 80-90: 0.24, 90-100: 0.32, 100-110: 0.16, 110-120: 0.2. What percentage of the students had scores from 90-100?

about 32%

Find P(# greater than 2 on the red die and 4 on the blue die OR 3 on the red die and sum of the numbers is greater than 6). Don't over count a. 1 b. 1/5 c. 6/36 d. 8/36 e. 1/4

c. 6/36

Determine whether the two events are disjoint (separate) for a single trial and why (choose A, B, C, or D. Event 1: A person believes that there needs to be a spending freeze Event 2: A person is opposed to increased funding for education a) The events are not disjoint. The first event is not the complement of the second b) The events are disjoint. They cannot occur at the same time c) The events are disjoint. The first event is the compliment of the second d) The events are not disjoint. They can occur at the same time

d) The events are not disjoint. They can occur at the same time.

Showing your work, find the mean and the 20% trimmed mean of the data set {18, 12, 15, 24, 21, 9, 27, 6, 3, 30}

mean = 16.5, trimmed mean = 16.5

Make a scatterplot, find the coefficient of determination. (x, y): (2, 10); (4, 14); (12, 30); (8, 22); (10, 26); (6, 18); (14, 34)

r = 1

How do you calculate the sample variance?

s²=(∑(x-mean)²)/(n-1)

76% of the people who are told that a product is improved will believe that it is improved. The remaining 24% believe it is just hype. Suppose a marketing study consisted of a random sample of 18 people who are given a sales talk about a new improved product. Compute the expected number of people who will believe the product is improved and the standard deviation of the resulting probability of distribution

µ = 13.68, σ = 1.81

A recent study on prisons found that about 15% of all prison parolees became repeat offenders. Christ is a social worker whose job is to console people on parole. Let us say that success means that a person does not become a repeat offender. Chris has been given a group of 5 parolees. What is the expected number of people who will not become repeat offenders? What is the standard deviation?

µ = 4.25, σ = 0.80