PSYC 7302 Module 4 pt. 2

The average time to complete a 10K race for a female runner is 64.61 minutes with a standard deviation of 5.18 minutes. Sarah completes her first 10K race in 58.24 minutes. What is Sarah's z-score? (Round your answer to 2 decimal places.)

-1.23

Suppose that foot length in inches of a randomly chosen adult male is a normal random variable with mean =11 and standard deviation = 1.5 What is the probability that a randomly chosen adult male will have a foot length either smaller than 6.5 inches or larger than 15.5 inches ?

0.003

Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. Suppose that to qualify for the Nationals, a woman must complete the 200-meter backstroke in less than 128 seconds. What proportion of competitive female swimmers will qualify for the Nationals? Give your answer to four (4) decimal places.

0.0314

According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica's z-score? (Round your answer to 2 decimal places.)

1.79

The number of days (X) after mailout it takes a utility company to receive payment for a customer's bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. There is a probability of 0.50 that a bill will be received later than ________ days after mailout. A. 13 B. 19 C. 25 D. 31 E. 37 F. 43 G. 49

D. 31

Suppose the scores on an exam are normally distributed with a mean μ = 75 points, and standard deviation σ = 8 points. The instructor wanted to "pass" anyone who scored above 69. What proportion of exams will have passing scores? A. 0.1587 B. 0.75 C. 0.2266 D. 0.7734 E. −0.75

D. 0.7734

Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. Suppose the fastest 6% of female swimmers in the nation are offered college scholarships. In order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than how many seconds? Give your answer in whole numbers.

130

In Texas, 30% of parolees from prison return to prison within 3 years. Suppose 15 prisoners are released from a Texas prison on parole. Assume that whether or not one prisoner returns to prison is independent of whether any of the others return to prison. Let the random variable X be the number of parolees out of 15 that return to prison within 3 years. What are the values of the parameters for the binomial random variable X? n = ________ p = ________

15; 0.30

According to the website nationalbikeregistry.com, at the campus of UC Berkeley 12% of registered bicycles are stolen each year. Suppose a random sample of 160 registered bicycles at UC Berkeley is selected. Let the random variable X be the number of bicycles that were stolen in the past year. What are the values of the parameters for the binomial random variable X? n = ________ p = ________

160; 0.12

According to the CDC, the rate of Cesarean births in the United States in 2013 was about 33%. Suppose a random sample of 200 births is selected. Let X be the number of Cesarean births out of all 200 births. What are the values of the parameters for the binomial random variable X? n = ________ 4 p = ________

200; 0.33

Suppose the scores on an exam are normally distributed with a mean μ = 80 points, and standard deviation σ = 10 points. Suppose that the top 90% of the participants can pass the exam. In order to pass the exam, a participant must earn at least what score?

67.2

Suppose the scores on an exam are normally distributed with a mean μ = 75 points, and standard deviation σ = 8 points. Suppose that the top 4% of the exams will be given an A+. In order to be given an A+, an exam must earn at least what score? Report your answer in whole numbers.

89

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below: X: the number of US residents (out of 50) with blood type AB. Y: the number of Australians (out of 40) with blood type AB. Z: the total number of individuals (out of 90) with blood type AB. Which of the following is true about the random variables X, Y, and Z? Check all that apply. A. X is a binomial random variable with n = 50 and p = 0.04 B. Y is a binomial random variable with n = 40 and p = 0.015 C. Z is a binomial random variable with n = 90 and p = 0.055

A & B

Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%. A random sample of 20 white males and 40 while females were chosen. Let X be the number of males (out of the 20) who are colorblind. Let Y be the number of females (out of the 40) who are colorblind. Let Z be the total number of colorblind individuals in the sample (males and females together). Which of the following is true about the random variables X, Y, and Z? Check all that apply. A. X is binomial with n=20 and p=.08. B. Y is binomial with n=40 and p=.01. C. Z is not binomial.

A, B, & C

The number of days (X) after mailout it takes a utility company to receive payment for a customer's bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. The probability is 0.997 that a bill will be received between which of the following number of days? A. (13, 49) B. (19, 43) C. (25, 37)

A. (13, 49)

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below: X: the number of U.S. residents with blood type AB Y: the number of Australians with blood type AB What is the probability that exactly 2 of the U.S. residents have blood type AB? (Note: Some answers are rounded) A. 0.2762 B. 0.04 C. 0.1334 D. 0.0988 E. 0.2646

A. 0.2762

The time it takes a surgeon to complete a laproscopic surgery to remove the gall bladder is normally distributed with a mean of 132.4 minutes and a standard deviation of 15.7 minutes. A patient's risk of complications is increased the longer he is in surgery. An unusually risky surgery is one that is in the top 4% of all surgery lengths. What is the minimum surgery length (in minutes) that would be considered unusually risky? Note: Answers are rounded to 1 decimal place. A. 159.9 minutes B. 104.9 minutes C. 147.5 minutes D. 247.4 minutes

A. 159.9 minutes

The lifetime in miles for a certain brand of tire is normally distributed with a mean of 22,000 miles and a standard deviation of 3,100 miles The tire manufacturer wants to offer a money-back guarantee so that no more than 3% of tires will qualify for a refund. What is the minimum number of miles the manufacturer should guarantee that the tires will last? A. 16,172 miles B. 27,828 miles C. 25,007 miles D. 15,800 miles

A. 16,172 miles

In the following random experiment, decide whether the random variable X is binomial or not: Approximately 1 in 10 people are left-handed. Let X be the number of people that are left-handed out of a random sample of 200 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. A. Binomial B. Not binomial

A. Binomial

When calculating the standard deviation of a population, the denominator should be: A X B N C n-1 D mu

B N

Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%. A random sample of 20 white males and 40 while females were chosen. Let X be the number of males (out of the 20) who are colorblind. Let Y be the number of females (out of the 40) who are colorblind. Let Z be the total number of colorblind individuals in the sample (males and females together). What is the probability that exactly 2 of the 20 males are colorblind? A. 0.08 B. 0.2711 C. 0.0519 D. 0.5422 E. 0.0159

B. 0.2711

Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. What is the completion time for the 200-meter backstroke for a female with a z-score of −1.64? (Round answer to 1 decimal place.) A. 130.8 B. 129.5 C. 152.5 D. 141.0

B. 129.5

In the following random experiment, decide whether the random variable X is binomial or not: A sample of 4 cards is selected without replacement from a standard deck of 52-cards, in which there are 26 red and 26 black cards. Let X be the number of cards that are red A. Binomial B. Not binomial

B. Not binomial

Left-handedness occurs in about 12% of all Americans. Males are slightly more likely than females to be left-handed, with 13% of males and 11% of females being left-handed. Suppose a random sample of 80 females and 100 males is chosen. Let X be the number of males (out of the 100) who are left-handed. Let Y be the number of females (out of the 80) who are left-handed. Let Z be the total number of left-handed individuals in the sample (males and females together). Which of the following is true regarding the random variables X and Y? A. Both X and Y can be well approximated by normal random variables. B. Only X can be well approximated by a normal random variable. C. Only Y can be well approximated by a normal random variable. D. Neither X nor Y can be well approximated by a normal random variable.

B. Only X can be well approximated by a normal random variable.

Approximately 1 in every 20 wizards like chocolate frogs. Let X be the number of wizards that like chocolate frogs out of a random sample of 400 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. Is the random variable X binomial or not?

Binomial

____ random variables have a fixed number of independent trials, notated n.

Binomial

with a mean of 82 and a standard deviation of 5. Harry, who took Professor Snape's class, scored an 88 on his potions exam. Harry's z-score is: Scores for Professor Snape's potions exam class follow a normal distribution A .88 B -2 C 1.2 D 2.1

C 1.2

The number of days (X) after mailout it takes a utility company to receive payment for a customer's bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. About 16% of bills will be received earlier than ________ days after mailout. A. 13 B. 19 C. 25 D. 31 E. 37 F. 43 G. 49

C. 25

Suppose the scores on an exam are normally distributed with a mean μ = 75 points and standard deviation σ = 8 points. What is the exam score for an exam whose z-score is 1.25? A. 65 B. 75 C. 85 D. 0.8944 E. 0.1056

C. 85

The binomial formula is the: A. The cdf of the binomial distribution B. The cdf of the normal distribution C. The pmf of the binomial distribution D. the pdf of the normal distribution

C. The pmf of the binomial distribution

Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%. A random sample of 20 white males and 40 while females were chosen. Let X be the number of males (out of the 20) who are colorblind. Let Y be the number of females (out of the 40) who are colorblind. Let Z be the total number of colorblind individuals in the sample (males and females together). Which of the following is true regarding the random variables X and Y? A. Both X and Y can be well approximated by normal random variables. B. Only X can be well approximated by a normal random variable. C. Only Y can be well approximated by a normal random variable. D. Neither X nor Y can be well approximated by a normal random variable.

D. Neither X nor Y can be well approximated by a normal random variable.

The standard normal table displays: A. The pdf of the binomial distribution B. The pdf of the normal distribution C. The cdf of the binomial distribution D. The cdf of the normal distribution

D. The cdf of the normal distribution

The number of days (X) after mailout it takes a utility company to receive payment for a customer's bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. The latest 2.5% of bills will be received more than how many days after mailout? A. 13 B. 19 C. 25 D. 31 E. 37 F. 43 G. 49

F. 43

A sample of 6 jellybeans are drawn without replacement from a bag of Bertie Bot's Every Flavor Bean containing 30 jellybeans. There are 15 pleasant flavored beans and 15 unpleasant flavored beans. Let X be the number of unpleasant beans. Is the random variable X binomial or not?

Not binomial

Approximately 1 in 5 people are avid readers. Let X be the number of people that are avid readers out of a random sample of 700 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. X is a binomial value, true or false.

True

Binomial random variables have a _____ probability of success for each trial, notated p.

constant

For binomial random variables, _______ notates the number of successful trials.

k

What is the mean and standard deviation of the standard normal distribution we use in the tables?

mean=0 SD=1

A report about the Starships that go from Hoth to Tatooine found that 75% of all starships arrive safely, the rest are intercepted by the Empire's Deathstar and handily shot down. Suppose a random sample of 90 starships is selected from all Starship rides in the past 30 days (over 700 starships). Let the random variable X be defined as the number of sampled starships that arrived. What is the value of the n parameter of the binomial random variable X? What is the value of the p parameter of the binomial random variable X?

n=9 p=.075

Binomial random variables have ______ n and p.

parameters