1. Before 1918, approximately 60% of the wolves in a region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.)

(a) Before 1918, in a random sample of 10 wolves spotted in the region, what is the probability that 7 or more were male?

What is the probability that 7 or more were female?

What is the probability that fewer than 4 were female?

(b) For the period from 1918 to the present, in a random sample of 10 wolves spotted in the region, what is the probability that 7 or more were male?

What is the probability that 7 or more were female?

What is the probability that fewer than 4 were female?

2. In a binomial situation, p + q = 1.00.

True

False    

In a sample of 1100  U.S.​ adults, 203 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​ adults, complete parts​ (a) through​ (c).

(a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as​ needed.)

​(b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is _______?(Round to three decimal places as​ needed.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.4 pounds, what is the probability that the sample mean will be each of the following?

Appendix A Statistical Tables

a. More than 58 pounds
b. More than 57 pounds
c. Between 55 and 58 pounds
d. Less than 55 pounds
e. Less than 49 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample mean will be more than 58pounds

b. enter the probability that the sample mean will be more than 57pounds

c. enter the probability that the sample mean will be between 55 and 58pounds

d. enter the probability that the sample mean will be less than 55 pounds

e. enter the probability that the sample mean will be less than 49 pounds

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.4 pounds, what is the probability that the sample mean will be each of the following?

Appendix A Statistical Tables

a. More than 59 pounds
b. More than 57 pounds
c. Between 55 and 58 pounds
d. Less than 54 pounds
e. Less than 49 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample mean will be more than 59 pounds

b. enter the probability that the sample mean will be more than 57 pounds

c. enter the probability that the sample mean will be between 55 and 58 pounds

d. enter the probability that the sample mean will be less than 54 pounds

e. enter the probability that the sample mean will be less than 49 pounds

A terrible new virus has been discovered amongst​ beef-cattle in Southern Alberta. It is estimated that  

44​%

of all​ beef-cattle are infected with this virus. A team of veterinarians have developed a simple test. Indications are that this test will show a positive result​ - indicating the​ beef-cow being tested has the virus​ - with a probability of

0.950.95.

​Unfortunately, this test has a​ false-positive probability of

0.060.06.

​(a) A​ beef-cow in Southern Alberta was randomly chosen and given this test. The test results were​ positive, indicating the​ beef-cow has the virus. What is the probability that this particular​ beef-cow actually does have the​ virus?

​(b) What is the probability that a​ beef-cow that tests negative for this​ virus, actually has the​ virus?

​(a) If the​ beef-cow tests positive for the​ virus, the probability that this​ beef-cow actually has the virus is

nothing.

​(Enter your answer to four​ decimals)

​(b) The probability that a​ beef-cow that tests negative for this​ virus, actually has the virus is

nothing.

​(Enter your answer to four​ decimals)

21.5% of flowers of a certain species bloom "early" (before May 1st). You work for an arboretum and have a display of these flowers

a) In a row of 35 flowers, what is the probability that 8 will bloom early?

b) In a row of 35 flowers, what is the probability that fewer than 9 will bloom early?

c) As you walk down a row of these flowers, how many flowers do you expect to have to observe (on average) in order to see the first one that blooms early? (Keep your answer as a decimal.)

d) In a row of 50 flowers, what is the probability that more than 8 will bloom early?

e) In a row of 50 flowers, what is the probability that between 8 and 14 (inclusive) will bloom early?

f) In a row of flowers, what is the probability that you will have to observe 6 flowers in order to see the first one that blooms early?

g) In a row of flowers, what is the probability that you will observe more than 7 flowers to see the first one that blooms early?

1) Suppose the scores of students on a Statistics course are Normally distributed with a mean of 542 and a standard deviation of 98. What percentage of the students scored between 542 and 738 on the exam? (Give your answer to 3 significant figures.)

2) A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 6 miles. Find the probability of the following events:

A. The car travels more than 69 miles per gallon.

Probability =

B. The car travels less than 59 miles per gallon.

Probability =

C. The car travels between 59 and 68 miles per gallon.

Probability =

3)

(1 point) Suppose that X is normally distributed with mean 85 and standard deviation 20.

A. What is the probability that X is greater than 118?
Probability =

B. What value of XX does only the top 18% exceed?
X =

1) One out of every 92 tax returns that a tax auditor examines requires an audit. If 50 returns are selected at random, what is the probability that less than 3 will need an audit? 0.0151 0.9978 0.0109 0.9828

2) Sixty-seven percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months? 0.142 0.550 0.692 0.450

3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line? No, as the probability of six having the correct shape is not unusual Yes, as the probability of six having the correct shape is not unusual No, as the probability of six having the correct shape is unusual Yes, as the probability of six having the correct shape is unusual

Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.)

(a) What is the probability that he will answer all questions correctly?


(b) What is the probability that he will answer all questions incorrectly?


(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.


Then use the fact that P(r ≥ 1) = 1 − P(r = 0).


Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference?

(d) What is the probability that Richard will answer at least half the questions correctly?

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 7.2% with a standard deviation of 15.7%. The relatively less risky fund promises an expected return and standard deviation of 3.9% and 6%, respectively. Assume that the returns are approximately normally distributed.

a-1. Calculate the probability of earning a negative return for each fund. (Round final answer to 4 decimal places.)Probability: Riskier fund and Less risky fund

a-2. Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return?

Less risky or fund Riskier fund

b-1. Calculate the probability of earning a return above 8.3% for each fund. (Round final answer to 4 decimal places.) Probability Riskier fund and Less risky fund

b-2. Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 8.3%?

Riskier fund or Less risky fund