Calculus and Above

Calculus Questions? Ask a Mathematician for Answers ASAP

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1. (5 points) In a certain town, 4% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

A. 1:24

B. 1:25

C. 24:25

D. 24:1

2. (5 points) Among the contestants in a competition are 43 women and 21 men. If 5 winners are randomly selected, what is the probability that they are all men?

A. 0.00267

B. 0.02114

C. 0.02778

D. 0.13691

3. (5 points) A tourist in France wants to visit 6 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?

A. 720

B. 1/720

C. 1/36

D. 1/6

4. (5 points) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.49, 0.42, 0.06 and 0.03, respectively. What is the mean of the given probability distribution?

A. 0.63

B. 0.59

C. 1.08

D. 1.5

5. (5 points) The standard deviation for the binomial distribution with n=40 and p=0.4 is:

A. 7.58

B. 6.73

C. 3.46

D. 3.10

6. (5 points) The probability that a person has immunity to a particular disease is 0.3. Find the mean number who have immunity in samples of size 18.

A. 5.4

B. 10.8

C. 9.0

D. 7.2

7. (5 points) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $120. What percentage of trainees earn less than $900 a month?

A. 9.18%

B. 40.82%

C. 90.82%

D. 4.75%

8. (5 points) For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 2 standard deviation above the mean.

A. 84.00%

B. 16.00%

C. 15.74%

D. 97.59%

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Express percents as decimals. Round dollar amounts to the nearest cent.

9. (15 points) Most of us hate buying mangos that are picked too early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of having 7% of the picked rot upon arrival at the packing facility. If the packing process is all done by machines without human inspection to pick out any rotten mangos, what would be the probability of having at most 2 rotten mangos packed in a box of 12?

10. We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance team of 5 has to by picked randomly from the crew of 7 boys and 3 girls.

a. (5 points) What is the probability that all 3 girls are picked in this team of 5?

b. (5 points) What is the probability that none of the girls are picked in this team of 5?

c. (5 points) What is the probability that 2 of the girls are picked in this team of 5?

11. (15 points) A soda company want to stimulate sales in this economic climate by giving customers a chance to win a small prize for every bottle of soda they buy. There is a 20% chance that a customer will find a picture of a dancing banana ( ) at the bottom of the cap upon opening up a bottle of soda. The customer can then redeem that bottle cap with this picture for a small prize. Now, if I buy a 6-pack of soda, what is the probability that I will win something, i.e., at least win a single small prize?

12. (15 points) A department store manager has decided that dress code is necessary for team coherence. Team members are required to wear either blue shirts or red shirts. There are 9 men and 7 women in the team. On a particular day, 5 men wore blue shirts and 4 other wore red shirts, whereas 4 women wore blue shirts and 3 others wore red shirt. Apply the Addition Rule to determine the probability of finding men or blue shirts in the team.

1. (5 points) In a certain town, 4% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

A. 1:24

B. 1:25

C. 24:25

D. 24:1

2. (5 points) Among the contestants in a competition are 43 women and 21 men. If 5 winners are randomly selected, what is the probability that they are all men?

A. 0.00267

B. 0.02114

C. 0.02778

D. 0.13691

3. (5 points) A tourist in France wants to visit 6 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?

A. 720

B. 1/720

C. 1/36

D. 1/6

4. (5 points) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.49, 0.42, 0.06 and 0.03, respectively. What is the mean of the given probability distribution?

A. 0.63

B. 0.59

C. 1.08

D. 1.5

5. (5 points) The standard deviation for the binomial distribution with n=40 and p=0.4 is:

A. 7.58

B. 6.73

C. 3.46

D. 3.10

6. (5 points) The probability that a person has immunity to a particular disease is 0.3. Find the mean number who have immunity in samples of size 18.

A. 5.4

B. 10.8

C. 9.0

D. 7.2

7. (5 points) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $120. What percentage of trainees earn less than $900 a month?

A. 9.18%

B. 40.82%

C. 90.82%

D. 4.75%

8. (5 points) For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 2 standard deviation above the mean.

A. 84.00%

B. 16.00%

C. 15.74%

D. 97.59%

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Express percents as decimals. Round dollar amounts to the nearest cent.

9. (15 points) Most of us hate buying mangos that are picked too early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of having 7% of the picked rot upon arrival at the packing facility. If the packing process is all done by machines without human inspection to pick out any rotten mangos, what would be the probability of having at most 2 rotten mangos packed in a box of 12?

10. We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance team of 5 has to by picked randomly from the crew of 7 boys and 3 girls.

a. (5 points) What is the probability that all 3 girls are picked in this team of 5?

b. (5 points) What is the probability that none of the girls are picked in this team of 5?

c. (5 points) What is the probability that 2 of the girls are picked in this team of 5?

11. (15 points) A soda company want to stimulate sales in this economic climate by giving customers a chance to win a small prize for every bottle of soda they buy. There is a 20% chance that a customer will find a picture of a dancing banana ( ) at the bottom of the cap upon opening up a bottle of soda. The customer can then redeem that bottle cap with this picture for a small prize. Now, if I buy a 6-pack of soda, what is the probability that I will win something, i.e., at least win a single small prize?

12. (15 points) A department store manager has decided that dress code is necessary for team coherence. Team members are required to wear either blue shirts or red shirts. There are 9 men and 7 women in the team. On a particular day, 5 men wore blue shirts and 4 other wore red shirts, whereas 4 women wore blue shirts and 3 others wore red shirt. Apply the Addition Rule to determine the probability of finding men or blue shirts in the team.

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