Stats hw 2

Find z such that 21% of the area under the standard normal curve lies to the right of z. (Round your answer to two decimal places.)

.81 review q14

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 86 and standard deviation σ = 20. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 125 (borderline diabetes starts at 125)

.9032 .8849 .7881 .0256 q32

Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 43.4 months and a standard deviation of 6.5 months. (a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.) (b) If Quick Start does not want to make refunds for more than 14% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

12.92% 37 months q34

(a) What percentage of the area under the normal curve lies to the left of μ? (b) What percentage of the area under the normal curve lies between μ − σ and μ + σ? (c) What percentage of the area under the normal curve lies between μ − 3σ and μ + 3σ?

50 68 99.7

What percentage of the area under the normal curve lies as given below? (a) to the right of μ (b) between μ - 2σ and μ + 2σ (c) to the right of μ + 3σ (Use 2 decimal places.)

50 95 .15

According to the empirical rule, approximately what percentage of the area under a normal distribution lies within 1 standard deviation? Within 2 standard deviations? Within 3 standard deviations?

68 95 99.7

What are the requirements for a probability distribution? (Select all that apply.)

Each probability takes on values between 0 and 1 inclusive. A description of all the values of the random variable x. The summation of the probabilities equal 1. Associated probabilities for each value of x.

(e) Consider two normal curves. If the first one has a larger mean than the second one, must it have a larger standard deviation as well? Explain your answer. (Q16)

No. The values of μ and σ are independent.

To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a third number. If you used the correct sequence of numbers, the lock opens. If the dial of the lock contains 7 numbers, 0 through 6, determine the number of different combinations possible for the lock. Note: The same number can be reused consecutively.

Review 5 343

List the criteria for a binomial experiment. (Select all that apply.)

The probability of success on each trial is constant. The experiment must include a fixed number of trials repeated under identical conditions. The trials are independent. The trials have exactly two possible outcomes.

What does the random variable of a binomial experiment measure?

The random variable measures the number of successes in n trials.

Any score with a value less than the population mean will have a negative z-score.

True

A normal distribution has μ = 24 and σ = 5. (a) Find the z score corresponding to x = 19 (b) Find the z score corresponding to x = 37 (c) Find the raw score corresponding to z = −3. (d) Find the raw score corresponding to z = 1.9.

a. -1 b. 2.6 c. 9 d. 33.5

Raul received a score of 75 on a history test for which the class mean was 70 with a standard deviation of 6. He received a score of 72 on a biology test for which the class mean was 70 with standard deviation 6. On which test did he do better relative to the rest of the class?

q 22 History

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.7 minutes and a standard deviation of 2.2 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.) (a) less than 10 minutes (b) longer than 5 minutes (c) between 8 and 15 minutes

q15

The University of Montana ski team has nine entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the nine team entrants achieve first, second, and third places?

q17

Are customers more loyal in the East or in the West? The following table is based on information from a recent study. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent regions of the United States. What is the probability that a customer chosen at random has the following characteristics? (Enter your answers as fractions.) (a) has been loyal 10 to 14 years (b) has been loyal 10 to 14 years, given that he or she is from the East

q18

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ≤ −0.23) Shade the corresponding area under the standard normal curve.

q23-25

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−1.23 ≤ z ≤ 2.64)

q26

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 41; σ = 16 P(50 ≤ x ≤ 70)

q29

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 35 and standard deviation σ = 11. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

q33

There is money to send three of seven city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of three council members can be selected from the seven who want to go to the conference?

review #4 35

According to Harper's Index, 50% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected. (a) What is the probability that 10 or more are serving time for drug dealing? (Round your answer to three decimal places.) (b) What is the probability that 5 or fewer are serving time for drug dealing? (Round your answer to three decimal places.) (c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)

review q10

Given that x is a normal variable with mean μ = 43 and standard deviation σ = 6.8, find the following probabilities. (Round your answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c) P(50 ≤ x ≤ 60)

review q13

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows. (a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.) (b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

review q8

Describe a normal probability distribution. (Select all that apply.)

symmetric around the mean most of the data fall within 3 standard deviations from the mean bell-shaped mean, median, and mode all equivalent

Find z such that 4.6% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.) 3.8% 3.4%

z = -1.68 z = 1.77 z= 1.82 q30