# STAT 200-Masterquiz7 solutions

1. A birth is selected at random. Define events B = {the baby is a boy} and F = {the mother had the flu during her pregnancy}. The events B and F are

A. disjoint and independent.

B. disjoint but not independent.

C. independent but not disjoint.

D. neither disjoint nor independent.

The events are independent but not disjoint (i.e. mutually exclusive) since they can both occur.

Points Earned: 1/1

Correct Answer: C

Your Response: C

2. For the following statement, determine if it is true or false. If two events A and B are mutually exclusive, they must also be independent.

A. True

B. False

False; Just the opposite: if mutually exclusive then independent. Think of the events being Male and being Female. These two events are mutually exclusive since you can only be in one of the events. However, knowing that you are in event Male automatically disqualifies you from being in event Female so the P(male) is dependent on P(female) and vice-versa

Points Earned: 1/1

Correct Answer: B

Your Response: B

3. According to the Penn State Fact Book [University Park], approximately 55% of first year students graduate in 4 years (this is based on the average of those full-time first-year students from 1999 and 2000 who graduated in 4 years) and the percentage of first-year full time undergraduate female students for Fall 2005 is approximately 45%. If a freshman student from last fall is chosen at random, what is the probability that the student is a female and will graduate in four years?

A. 25%

B. 100%

C. 50%

The answer is found by taking 55% times 45% which comes to roughly 25%

Points Earned: 1/1

Correct Answer: A

Your Response: A

4. According to the Penn State Fact Book for Enrollment by Ethnicity Fall 2005 [University Park], in a class of 30 students, there would be 17 males and 13 females. Let us say that out of these 30 students five are A students, three of which are males. If a student is chosen at random, what is the probability of choosing a male or an A student?

A. 19/30

B. 17/180

C. 11/15

You are asked to find P(M or A) = P(M) + P(A) - P(A and M). Drawing a Venn Diagram such as the one found at See Venn helps trememdously in seeing how to solve this problem. P(M) = 17/30, P(A) = 5/30 and (M and A) = 3/30. Substituting these into the equation for P(M and A) results in 17/30 + 5/30 - 3/30 = 19/30.

Points Earned: 1/1

Correct Answer: A

Your Response: A

5. Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment. Five percent of all VCRs manufactured by a large electronics company are defective. Three VCRs are randomly selected from the production line of this company. The selected VCRs are inspected to determine whether each of them is defective or good.

A. NOT Binomial

B. Binomial

Binomial - all conditions are satisfied

Points Earned: 1/1

A. disjoint and independent.

B. disjoint but not independent.

C. independent but not disjoint.

D. neither disjoint nor independent.

The events are independent but not disjoint (i.e. mutually exclusive) since they can both occur.

Points Earned: 1/1

Correct Answer: C

Your Response: C

2. For the following statement, determine if it is true or false. If two events A and B are mutually exclusive, they must also be independent.

A. True

B. False

False; Just the opposite: if mutually exclusive then independent. Think of the events being Male and being Female. These two events are mutually exclusive since you can only be in one of the events. However, knowing that you are in event Male automatically disqualifies you from being in event Female so the P(male) is dependent on P(female) and vice-versa

Points Earned: 1/1

Correct Answer: B

Your Response: B

3. According to the Penn State Fact Book [University Park], approximately 55% of first year students graduate in 4 years (this is based on the average of those full-time first-year students from 1999 and 2000 who graduated in 4 years) and the percentage of first-year full time undergraduate female students for Fall 2005 is approximately 45%. If a freshman student from last fall is chosen at random, what is the probability that the student is a female and will graduate in four years?

A. 25%

B. 100%

C. 50%

The answer is found by taking 55% times 45% which comes to roughly 25%

Points Earned: 1/1

Correct Answer: A

Your Response: A

4. According to the Penn State Fact Book for Enrollment by Ethnicity Fall 2005 [University Park], in a class of 30 students, there would be 17 males and 13 females. Let us say that out of these 30 students five are A students, three of which are males. If a student is chosen at random, what is the probability of choosing a male or an A student?

A. 19/30

B. 17/180

C. 11/15

You are asked to find P(M or A) = P(M) + P(A) - P(A and M). Drawing a Venn Diagram such as the one found at See Venn helps trememdously in seeing how to solve this problem. P(M) = 17/30, P(A) = 5/30 and (M and A) = 3/30. Substituting these into the equation for P(M and A) results in 17/30 + 5/30 - 3/30 = 19/30.

Points Earned: 1/1

Correct Answer: A

Your Response: A

5. Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment. Five percent of all VCRs manufactured by a large electronics company are defective. Three VCRs are randomly selected from the production line of this company. The selected VCRs are inspected to determine whether each of them is defective or good.

A. NOT Binomial

B. Binomial

Binomial - all conditions are satisfied

Points Earned: 1/1

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