Stat quiz
A recent statistics exam yielded the following 25 scores. Construct a frequency table with the class limits shown below. 44 45 51 55 59 63 63 67 68 74 77 77 77 79 80 81 82 86 87 87 89 90 91 96 97
Answer is C (class limits. frequency) 41-50 2 51-60 3 61-70. 4 71-80 6 81-90 7 91-100 3
What is the sample space for flipping a fair coin 3 times? A. HHH HTH THT TTT B. HHH HHT HTH THH TTH THT HTT TTT C. HHH HHT HTH THH TTT D. HHT HTH THH TTH THT HTT
Answer. B
The following uniform distribution describes the wait time (in minutes) for passengers of the bus at a stop at the airport. What is the probability that a randomly selected passenger will wait between 5 and 10 minutes? A. 5/10 B. 5/9 C. 4/9 D. 4/10
Answer: B Calculate the area of the region between 5 and 10. It is a rectangle: (10-5)x(1/9) = 5/9.
A list of 5 pulse rates is 70, 64, 80, 74, and 92. What is the median for this list? a. 74 b. 76 c. 77 d. 80
Answer A. Using the definition of the median...the middle value in a set of numbers that have been arranged in order from smallest to largest
Which of the following lists all parts of the five-number summary? A. Mean, Median, Mode, Range, and Total B. Minimum, Quartile 1, Median, Quartile 3, and Maximum C. Smallest, Q1, Q2, Q3, and Q4 D. Minimum, Maximum, Range, Mean, and Median
Answer B. Based on the definition of 5-number-summary...consists of the smallest data value, the first quartile, the median, the third quartile, and the largest data value
A normal curve table tells you that the probability lying below z = -1 is .1587. This can be interpreted as: A 15.87% of the area of the curve lies below z = -1 B 15.87% of the area under the curve lies at or below z = -1 C A random selection from the population has a 15.87% chance of being below z = -1 D All choices are correct.
Answer D.
Elizabeth asks her friends how many brothers and/or sisters they have at home. What type of data is she collecting? a. Numerical b. Categorical c. None of these answers are correct d. Statistical
Answer is A
The histograms below show the scores for Mrs. Smith's first and second block classes at Red Rock Middle School Compare the histograms using the following information: 69 and above is passing • 68 or below is failing Which of the following statements is true? A) The number of students that passed the test is the same in both classes. B) More students passed in the first block than in the second block. C) More students passed in the second block than in the first block. D) Cannot be determined based on the graphs given.
Answer is A
If the variance of a data set is correctly computed with the formula using n-1 in the denominator, which of the following is true? A. the data set is a sample B. the data set is a population c. the data set could be either a sample or a population D. the data set is from the census e.none of the above
Answer is A (Use the definition of sample variance) a measure of the degree to which the numbers in a list are spread out..The variance will be small if the numbers in a list are all close to the expected values. If they are far away, the variance will be large. Sample variance is given by the equation. s 2 = ∑ ( O − E ) 2 n − 1.
A list of pulse rates is 70, 64, 80, 74, 92. What is the median for this list?
Answer is A (74) The middle value of the sorted data: 64, 70, 74, 80, 92
What do we call a part of a population used to describe the whole group? a. Population b. Sample c. Statistic d. Parameter
Answer is B
the following is data shows prices of meal options at Bob's burgers. prices of meal options at Bob's burgers 6 7 7 8 9 14 14 14 15 15 15 15 16 16 17 which histogram correctly displays the information above?
Answer is B (6-8=4, 9-11=1, 12-14=3, 15-17=7) (A is incorrect because 0-5 does not have data values, C is incorrect because it skipped 9-14, D is incorrect because its widths are not equal)
following is a pie chart that presents the percentages spent by a certain household on its five largest annual expenditures. What percentage of the money spent was pent on food , housing, and utilities?
Answer is B (food-27.7%, housing-24.8%, and utilities-12.9%, add them all up=65.4%)
The histogram below shows the scores for Mrs smiths first block class at Red Rock Middle School If an 85 is the lowest score a student can earn to receive a B, how many students received at least a B?
Answer is C (10)
Based on the following sample of ages (in months) of 18 children at a daycare: 18 19 22 22 24 24 25 26 28 29 29 30 31 32 35 36 36 42 the 25th percentile , 75th percentile and in interquartile range for this data set are
Answer is C (24, 32, 8) Calculate the two quartiles. The range = maximum - minimum
The following frequency distribution presents the frequency of passenger vehicles that pass through a certain intersection from 8:00am to 9:00am on a particular day vehicle type. Frequency motorcycle 5 sedan 95 SUV 65 Truck 30 construct a frequency bar graph for the data
Answer is C (the bar graph shows the motorcycle at 5, the sedan at 95, SUV at 65, and truck at 30..the highest point on frequency side is 100).
A study of 1106 college students asked about their preference for online resources. The following relative frequency distribution was determined as a result of the survey. resource relative frequency Google 0.736 library database. 0.136 Wikipedia 0.095 other 0.034 Of the 1106 students who participated in the survey, approximately how many chose Google or Google Scholar? A. 34 B. 292 C. 736 D. 814
Answer is D
The following pie chart presents the percentages of fish caught in each of four ratings categories. match this pie chart with its corresponding pare-to-chart (pompano 37.2%, bluefish 25.6%, flounder 27.9%, striped bass 9.3%)
Answer is D (the highest relative frequency is 0.4, the pompano is 0.37, the bluefish is 0.25, the flounder is 0.27, and the striped bass is 0.09)
A national random sample of 20 ACT scores from 2010 is listed below. Calculate the sample mean and standard deviation. 12 12 13 14 17 17 17 18 18 19 22 23 23 25 26 26 26 29 30 30 a. 20.50, 5.79 b. 20.50, 5.94 c. 20.85, 5.79 d. 20.85, 5.94
Answer is D You can use IntroStatsApps (descriptive statistics) to get his answer.
calculate the mean number of children per family for the sample from the following table Number of children. number of families 0 8 1 16 2 22 3 14 4 6 5 4 6 2 a. 1.91 b. 2.47 c. 3.14 d. 2.19
Answer is D You need to understand the frequency table to find the mean. For example, 8 families have no child, 16 families have one child, and 22 families have 2 children, following this pattern, you can find the total number of children and families. (8x0 + 16x1 + 22x2 + 14x3 + 6x4 + 4x5 + 2x6)/ (8+16+22+14+6+4+2) = 2.19.
The height of an adult male is known to be normally distributed with a mean of 175 cm and a standard deviation of 6 cm. We are interested in the 75th percentile in this distribution of heights. Let Q3 be denoted as the 75th percentile. Then Q3 can be solved from which of the following equations? A. 𝑄3 − 175 /6 = 0.675 B. 𝑄3 − 175 /36 = 0.675 C. 𝑄3 − 175 /6 = 0.75 D. 𝑄3 − 175 /6 = −0.7
Answer: A
Which of the following random variables should be considered continuous? A. The time it takes for a randomly chosen woman to run 100 meters. B. The number of brothers a randomly chosen person has. C. The number of cars owned by a randomly chosen adult male. D. The number of orders received by a mail-order company in a randomly chosen week.
Answer: A Time is a typical continuous variable. B-C are counts (number of ....).
Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Which of the following transformations converts this general normal distribution to the standard normal distribution, A). Z = (X - 63.6)/2.5 B). Z = (X - 2.5)/63.6 C). Z = 2.5 X + 63.6 D). Z = 63.6X + 2.5
Answer: A, Z = (X - 63.6)/2.5
What measure of the center was most affected by the outlier? A. mean B. median C. mode D. IQR
Answer: A. Understand the definition of mean and other measures..the average of a set of numbers..Add up all the numbers in the set Divide the sum by the total number of numbers in the set
uppose X follows a normal distribution with a mean of 5 and a variance of 9. After zscore transformation, Probability P(X ≤ 8) is equal to A P(Z ≤ 1) B P(Z ≤−1) C P(Z ≤ 0.6) D P(Z ≤−0.6)
Answer: A. Z = (8 - 5) / 9 = 3/3 = 1.
The table below reflects the student population at a fictional high school, where lower classmen refer to freshmen and sophomores and upperclassmen refer to juniors and seniors. Randomly select a male student, what is the probability that the student is an upperclassman? a. 197/438 b. 213/402 c. 197/410 d. 197/840
Answer: A. note that the selected student is restricted to male students
Suppose X is normally distributed with a mean of 5 and a standard deviation of 0.4. Assume that P(X ≤ X0) = P(Z ≤ 1.3). Which of the following equations should be solved to get the value of X0? A. X0 = 1.3x0.4 + 5 B. X0 = 1.3x0.4 - 5 C. X0 = 1.3x5 + 0.4 D. X0 = 1.3x5 - 0.4
Answer: A. solve X0 from 1.3 = (X0 - 5)/0.4
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 0 C at the freezing point of water. Tests on a large sample of these instruments reveal that the freezing point of water is around zero (some thermometers give positive degrees, some thermometers give negative degrees), Assume that the mean reading is 0 0 C and the standard deviation of the readings is 1.00 C. Assume further that the readings are normally distributed. Find the 3 rd percentile of the thermometer readings. A. 0.585 B. 0.675 C. 0.749 D. 0.7517
Answer: B since P(Z < Zo)=0.75 Answer: Zo= 0.675
You decide to conduct a survey of families with two children. You are interested in counting the number of boys (out of 2 children) in each family. Is this a random variable, and if it is, what are all its possible values? A. Yes, it is a random variable, and its values can be 1 and 2. B. Yes, it is a random variable, and its values are 0, 1, or 2. C. Yes, it is a random variable, and its values can be 2 or 4. D. No, it is not a random variable since it is not random.
Answer: B Use the definition of the random variable. a numerical value that represents the outcome of a probability experiment.
The time that it takes a WCU student to find parking once they have arrived on campus is approximately normally distributed with a mean of 25 minutes and a standard deviation of 5 minutes. If a student arrives on campus at 8:15 AM, we want to find the probability that the student will find parking before 8:45 AM. Which of the calculations is correct? A. 𝑃(𝑋 < 45 ) = 𝑃(𝑍 < 4) ≈ 1 B. 𝑃(𝑋 > 15 ) = 𝑃(𝑍 > −2) ≈ 0.9772 C. 𝑃(𝑋 < 30 ) = 𝑃(𝑍 < 1) ≈ 0.8413 D. 𝑃(𝑋 > 30 ) = 𝑃(𝑍 > 1) ≈ 0.1587
Correct Answer: C.
A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with a mean of 3 cm and a standard deviation of 0.1 cm. The specifications call for corks with diameters between 2.9 and 3.1 cm. A cork not meeting specifications is considered defective. We need to use the zscore transformation before using the standard normal distribution table. Which of the following calculations for the proportion of good corks is correct? A. 𝑃(2.9 < 𝑇 < 3.1) = 𝑃(−1 < 𝑍 < 1) = 0.8413 B. 𝑃(2.9 < 𝑇 < 3.1) = 𝑃(−1 < 𝑍 < 1) = 0.6826 C. 𝑃(2.9 < 𝑇 𝑜𝑟 𝑇 < 3.1) = 𝑃(−1 < 𝑍 𝑜𝑟 𝑍 < 1) = .3413 D. 𝑃(3.1 < 𝑇 𝑜𝑟 𝑇 < 2.9) = 𝑃(1 < 𝑍 𝑜𝑟 𝑍 < −1) = 0.3174
Answer: B.
Three unbiased coins are tossed. What is the probability of getting at least two heads? A) 6/8 B) 4/8 C) 7/8 D) 3/8
Answer: B. Hint: list all possible outcomes in the sample space. This is essentially the same as the example of the "three-kid" problem we worked on in class.
The table below reflects the student population at a fictional high school, where lowerclassmen refer to freshmen and sophomores and upperclassmen refer to juniors and seniors. Randomly select a student, what is the probability that the student is an upper-classman student? A. 430/840 B. 410/840 C. 213/410 D. 197/840
Answer: B. Randomly select a student from the population (all students).
For a normal distribution with a mean of 480 and a standard deviation of 32, find the value of Q2 (2 nd quartile, or median). A 458 B 480 C 500 D It depends on the size of the population.
Answer: B. The median (2nd quartile) of the standard normal distribution is Z = 0. That is, the median of the above normal distribution is (X0 - 480)/32 = 0, implies that X0 = 480.
The box-and-whisker plot below represents the results of test scores in a math class. What do the scores 65, 85, and 100 represent? A. Q1 , median, Q3 B. Q1 , Q3 , maximum C. median, Q1 , maximum D. minimum, median, maximum
Answer: B. Understand the structure of the box-plot
If the mean is larger than the median when A. The distribution is symmetric (bell-shaped) B. The distribution is skewed to the right (positively skewed) C. The distribution is skewed to the left (negatively skewed) D. The distribution is approximately normal.
Answer: B. Understanding the definition of the three central tendency measures. (mean, median, and mode)
On an intelligence test with a mean of 100 and a standard deviation of 15, Jamie scored 85. What is Jamie's z-score? a. -2 b. -1 c. 1 d. 2
Answer: B. Using the definition of z-score..a statistical measurement that shows how far a data point is from the average of a group of data
Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. What is the probability that a randomly selected customer will wait for exactly 5 minutes? A. 5/8 B. 3/8 C. 0 D. 1/8
Answer: C This is a uniform distribution. It is a continuous random variable. The probability of taking a single value is always 0.
Which of the following is NOT a property of a random variable? A. The sum of the probabilities of a discrete random variable is equal to 1. B. The distribution function of a random variable cannot be negative. C. A random variable must be less than or equal to 1 and greater than or equal to 0. D. A random variable can be discrete or continuous.
Answer: C Use the definition of the random variable.
Assume the density curve of a continuous random variable is given below. A, b, c, d, and e are four distinct values of the random variable. Let E = {a, b, c, d, e}. Find the probability P(E). A. 1/5 B. 1/3 C. 0 D. 1/(a+b+c+d+e)
Answer: C. The density curve indicates the continuity of the random variable. The probability of observing individual values is always 0. P(a) = P(b) = P(c) = P(d) = P(e) = 0. Therefore, the sum of these probabilities is also 0.
Which of the following is not a measure of variability in a data set? A. IQR (Inter Quartile range) B. Variance C. Upper quartile D. Standard deviation
Answer: C. Understand the definition of variability measures...describe how spread out a set of data is...how far apart data points lie from each other and the center of a distribution.
The box-and-whisker plot shown below represents the number of magazine subscriptions sold by members of a club. Which statistical measures do points B, D, and E represent, respectively? A. minimum, median, maximum B. first quartile, median, third quartile C. first quartile, third quartile, maximum D. median, third quartile, maximum
Answer: C. Understand the structure of the box-plot. (the box plot is a geometric representation of the five-number summary) (a box that spans the interquartile range (IQR) with a line inside marking the median, and lines extending from the box to the minimum and maximum values (whiskers)
If you got a 79 on a test in a class with a mean score of 85 and a standard deviation of 4.8, the zscore of your test score would be A 1.25 B -2.50 C -1.25 D 2.5
Answer: C. Z = (79 - 85)/4.8 = -4/4.8 = - 6/4.8 = - 1.25
Suppose a normally distributed random variable x has a mean of 100 and P(x < 90) = 0.20. What is the probability that x is between 90 and 110? Ie. What is P(90 < x < 110)? [Draw a density curve and label the values, then you can see the region you want to find the area.] A 0.2 B 0.3 C 0.4 D 0.5 E 0.6
Answer: D Both tail areas are equal to 0.2. The middle area is 1- 0.4 = 0.6. The correct answer is E.
Assume that the time required to receive confirmation that an electronic transfer has occurred is uniformly distributed between 30 and 90 seconds. What is the probability that a randomly selected transfer will take less than 75 seconds? A. 15/60 B. 15/90 C. 30/90 D. 45/60
Answer: D Use the area formula of the rectangle to find the probability: height = 1/(90-30) = 1/60, width = (75 - 30) = 45 ("less than"). The probability = 45/60.
Find the z-score in the standard normal distribution such that the area to the right of z is 0.12. A. - 1.175 B. 0.88 C. - 0.88 D. 1.175
Answer: D since p (z < Zo)=0.88 answer: Zo =1.175
A discrete random variable has the probability distribution seen below. What is the probability that x is greater than 2? A. 0.10 B. 0.20 C. 0.80 D. 0.70
Answer: D. P(x>2 ) = P(x=3) +P(x=4) + P(x=5) = 0.25 + 0.3 + 0.15 = 0.7
