HW 3&4 for exam 2

c

(Fine the z-score correspond to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary.) A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. a. -1.6; unusual b. -17.6; unusual c. -1.6; not unusual d. 1.6; not unusual

d

(Round your answer to one more decimal places than the original data) The numbers listed below represent the amount of precipitation (in inches) last year in six different US cities: 14.7, 15.1, 31.6, 42.6, 17.7, 18.8 a. 37.1 in b. 3924.2 in c. 3290.0 in d. 11.26 in

d

(Use the empirical formula to solve). At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0. 6. What percentage of students at the college have a GPA between 2.4 and 3.6? a. 95% b. 99.7% c. 84.13% d. 68%

c

A 6-sided die is rolled. Find P(3 or 5) a. 1/6 b. 2 c. 1/3 d. 1/36

d

A casino claims that its roulette wheel is truly random. What should that claim mean? a. The same number will not come up twice in a row b. The probabilities of all numbers will add up to 1 c. Every number will occur before any numbers repeat d. Every number is equally likely to occur

c

A family has 4 children; record the number of boys. Which of the following is the sample space for the number of boys in the family? a. (1,2,3,4) b. (1,2,3) c. (0,1,2,3,4) d. (0,1,2,3)

b

An internet company that sells piercing jewelry, keeps transaction records on it sales. At a recent sales meeting, one of the staff presented the accompanying histogram of the postal codes of the last 500 customers, so that the staff might understand where sales are coming from. Comment on the usefulness and appropriateness of the display. a. The histograms bins are too wide to be useful b. The variable being graphed is categorical. A histogram should be constructed using categorical values, so a bar chart or pie chart would be more appropriate c. The histogram is appropriate for the given data and has been constructed correctly.

b

Can disjoint events ever be independent? Explain. Choose the correct answer below. a. No, because once one of a pair of disjoint events has occurred, the other is guaranteed to happen. b. No, because once one of a pair of disjoint events has occurred, the other is impossible. c. Yes, because the occurrence of one of a pair of disjoint events does not affect the probability of the other event. d. No because once one of a pair of disjoint events has occurred, the other is more likely.

a

police report that 78% of divers are given a breath test, 36% a blood test, and 22% both test. Find P(breath test | blood test). a. 0.22/0.36 b. 0.14/0.36 c. 0.22/0.78 d. 0.78/1.0

a

roll two dice; record the smaller number. What is the sample space for the smaller number when two dice are rolled? a. (1,2,3,4,5,6) b. (1,2,3,4,5) c. (0,1,2,3,4,5,6) d. (0,1,2,3,4,5)

b

Our survey found that 56% of college students live on campus, 62% have a campus meal program, and 42% do both. In this example, what would be the denominator of the fraction if we wanted to find the conditional probability P(meal plan | live on campus)? a. .42 b. .56 c. there is not enough information to answer this question d. .62

a

Suppose that 65% of families living in a certain country own a car and 19% own an SUV. The addition rule might suggest, then, that 84% of families own either a car or an SUV. What's wrong with that? a. A family may own both or car and a SUV. The events are not disjoint, so the addition rule does not apply b. The sum of the probabilities of the two given events does not equal 1, so this is not a legitimate probability assignment c. The reasoning is correct, thus 84% of families own either a car of an SUV d. If one family owns a car or an SUV, it can influence another family to also own a car or an SUV. The events are not independent, so the addition does not apply.

a

Suppose your statistic professor reports test grades as z-scores, and you got a score of 2.20 on an exam. Write a sentence explaining what that means. a. The score was 2.20 standard deviations higher than the mean score in the class b. The scare was 2.20 points lower than the mean score in class c. The score was 2.20 standard deviations lower than the mean sure in the class d. The score was 2.20 points higher than the mean score in the class

a

The histogram shows the amount of oil produced (in gallons) from an acre of land in a country for 48 different crops. Which summary statistics would you choose to summarize the center and spread in these data? Why? a. The median and IQR because the distribution is strongly skewed b. The mean and IQR because the distribution is strongly skewed c. The median and standard deviation because the distribution is unimodal and symmetric d. The mean and standard deviation because the distribution is unimodal and symmetric

a

The histogram shows the distribution of the prices of small, plain pizza (in $) for 298 weeks in a large city. Which summary statistics would you choose to summarize the center and spread in these data? a. The median and standard deviation because the distribution is unimodal and symmetric b. The median and IQR because the distribution is strongly skewed c. The mean and IQR because the distribution is strongly skewed d. The mean and standard deviation because the distribution is unimodal and symmetric

a

The histogram shows the neck sizes (in inches) of 263 men recruited for a health study. Is the mean closer to 13, 15, or 17 inches? Why? a. The mean is closest to 15 inches because that's the balancing point of the histogram b. The mean is closest to 13 inches because that the balancing point of the histogram c. The mean is closest to 17 inches because it splits the histogram into two equal areas d. The mean is closest to 15 inches because it it splits the histogram into two equal areas

c

The histogram shows the neck sizes (in inches) of 263 men recruited for a health study. Is the standard deviation closer to 1in, 3 inches, or 5 inches? Explain. a. The standard deviation is closest to three inches because a typical value lies about 3 inches from the mean b. The standard deviation is closest to 5 inches because a typical value lies about 5 inches from the mean c. The standard deviation is closest to 1 inch because a typical value lies about 1 inches from the mean

c

Which of the following cannot be a probability? a. 1 b. ½ c. -1 d. 0

e

Which of the following statement is TRUE about a z-score? a. A z-score tells us how many standard deviations a value is from the mean b. Z-scores standardize a dataset c. Z-scores have a mean of 0 and a standard deviation of 1 d. A z-score is a measure of how extreme or typical a data value is e. All of the above

b

You estimate that there is an 80% change of answering any individual question correctly. The test is 5 questions long. If you wanted to find the probability you answer all the questions incorrectly, what could you do? a. 0.2+0.2+0.2+0.2+0.2 b. 0.2x0.2x0.2x0.2x0.2 c. 0.8x0.8x0.8x0.8x0.8 d. 1-.08

b

determine whether the following statement is true or false. It is always true that P(A|B)=P(B|A). a. true b. false

b

A friends tells you about a recent study dealing with the number of years of teaching experience among current college professor. He remembers the mean but cannot recall whether the standard deviation was 6 months, 6 years or 16 years. Tell him which one it must have been and why. a. The standard deviation is 16 years because some college professors teach for over 50 years, and the study will have to account for those professors b. The standard deviation is 6 years because 6 months would result in for too small interval of reasonable years and 16 years would result in far too many c. The standard deviation is 6 months because both 6 years and 16 years would result in far too large an interval of reasonable years.

d

A poll classified respondents by gender and political party, as shown in the table. Is the party affiliation independent of sex? Explain. a. Yes, because the outcome of one does not influence the probability of the other b. Yes, because there are no common outcomes c. No, because there are outcomes that are common between them d. No, because the outcome of one influences the probability of the other

a

A survey of 12 gas stations produced the following prices for a gallon of regular gasoline. 2.279, 2.159, 2.119, 2.069, 2.139, 2.079, 2.199, 2.199, 2.029, 2.089, 2.029, 2.089 Is the data symmetric, skewed to the right, or skewed to the left? a. The distribution is skewed to the right b. The distribution is skewed to the left c. The distribution is symmetric

b

Find the indicated probability. A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue). a. 3/10 b. 7/10 c. 10/7 d. 7

a

The plastic arrow on a spinner for a child's game stops rotating to point at a color that will determine what happens next. Are the given probabilities assignments for all 4 colors possible? a. A b. D c. C d. B

a

The probabilities that an adult man has high blood pressure and/or high cholesterol are shown in the table. Are high blood pressure and high cholesterol independent? Explain a. No, because the outcome of one influences the probability of the other b. Yes, because there are no common outcomes c. No, because there are outcomes that are common between them d. Yes, because the outcome of one does not influences the probability of the other

b

The stem and leaf display shows the number of home runs hit by Mark during the 1986-1999 season. Describe the distribution, mentioning its shape and any unusual features. a. The distribution is symmetric b. The distribution is skewed to the right c. The distribution is skewed to the left

b

The table below shows the 5-number summary for the run times in minutes of the 100 highest grossing movies of last year. Are there any outliers in the data? Explain. a. yes, because while the maximum is within 1.5 IQRs of the upper quartiles, the minimum is beyond 1.5 IQRs below the lower quartile b. no, because the minimum is within 1.5IQRs of the lower quartile and the maximum is within 1.5 IQRs of the upper quartiles c. no, because the minimum is beyond 1.5 IQRs below the lower quartiles, and the maximum is beyond 1.5 IQRs above the upper quartile.