Q: Suppose a random sample contains 60 kids, 25% of whom have a FREE logo t-shirt. What is the probability that you find two free tees in a group of 4?

$$P = 6 \times (0.25)^2$ \times (0.75)^2$

Q: A regression analysis between students' GPA and their salary after graduation yields the fitted regression equation: $$\text{salary} = 2050 + 1300 \times \text{GPA}. $$What is the predicted salary for a student with a GPA of 3.5?

$$2050 + 1300 \times 3.5 = 6600$$

Q: If the number of repairs needed each year is independent, what is the standard deviation of the total number of repairs needed over three years?

$$\sqrt{3} \times 1.3 \approx 2.25$$

Question 1

A survey of AP Stats students recorded gender and whether the student was left or right-handed. If the numbers were assumed to be a tally for the entire class, if it turned out that handedness was independent of gender, how many of the AP Stat students were lefty girls?

Accepted Answer

7

Question 2

Suppose a random sample contains 60 kids, 25% of whom have a FREE logo t-shirt. What is the probability that you find two free tees in a group of 4?

Accepted Answer

$$P = 6 	imes (0.25)^2$ 	imes (0.75)^2$

Question 3

A national study found that the average family spent $$822 a month on groceries, with a standard deviation of 62. $$The average amount spent on nonfood items (household supplies, etc.) was $$231, with a standard deviation of 21. If $$these two amounts are independent, what is the standard deviation of the total monthly spending for a family?

Accepted Answer

$$\sqrt{62^2$ + 21^2$} = 65.5$$

Question 4

Suppose we know that 57% of college students eat breakfast in the morning. In a small group of 5 students, what is the probability that at least one of them did not eat breakfast that morning?

Accepted Answer

$$1 - (0.57)^5$

Question 5

A certain university is interested in the average weight of male students. The university randomly samples 100 students and finds the sample mean weight is 170 lbs with a standard deviation of 15 lbs. What is the standard error of the sample mean?

Accepted Answer

$$\frac{15}{\sqrt{100}} = 1.5$$

Question 6

The Central Limit Theorem (CLT) only applies to the sampling distribution of means under which of the following conditions?

Accepted Answer

The sample size is large enough, typically $$n \geq 30$$

Question 7

A factory has to randomly select items for inspection. To inspect a representative sample of 100 items, which sampling method is most likely to avoid bias from how the lot is arranged?

Accepted Answer

Simple random sample

Question 8

A researcher wants to compare the performance of three types of pain relievers in volunteers with chronic arthritis. The researcher divides 60 subjects into three groups and randomly assigns each group to one pain reliever. Twenty minutes later they rate their pain relief. What is the experimental design?

Accepted Answer

Completely randomized design

Question 9

A regression analysis between students' GPA and their salary after graduation yields the fitted regression equation: $$	ext{salary} = 2050 + 1300 	imes 	ext{GPA}. $$What is the predicted salary for a student with a GPA of 3.5?

Accepted Answer

$$2050 + 1300 	imes 3.5 = 6600$$

Question 10

In a study, 40% of traffic accidents involved alcohol, 30% involved speeding, and 15% involved both. What is the probability that an accident involved alcohol or speeding?

Accepted Answer

$$0.40 + 0.30 - 0.15 = 0.55$$

Question 11

A fast food restaurant just issued a new three-year service contract for their kitchen equipment. The contract covers up to 5 repairs per year. The expected number of repairs needed in a year is 2.2, with a standard deviation of 1.3. What is the expected number of repairs needed over the three-year term?

Accepted Answer

$$2.2 	imes 3 = 6.6$$

Question 12

If the number of repairs needed each year is independent, what is the standard deviation of the total number of repairs needed over three years?

Accepted Answer

$$\sqrt{3} 	imes 1.3 \approx 2.25$$

Question 13

The American Red Cross says that about 15% of the U.S. population has Type B blood. Suppose a blood drive is being held at a university. What is the probability that none of the first 20 blood donors at the blood drive have Type B blood?

Accepted Answer

$$(0.85)^{20}$$

Question 14

What is the probability that at least 1 of the first 20 blood donors at the blood drive have Type B blood?

Accepted Answer

$$1 - (0.85$$)^{20}$$

Question 15

A box of Almond Crunch cereal contains a mean of 13 ounces with a standard deviation of 0.3 ounces. If a random sample of 12 cereal boxes is selected, what is the probability that the mean weight of the sample exceeds 13.2 ounces?

Accepted Answer

$$P(Z \u003e \frac{13.2 - 13}{0.3/\sqrt{12}})$$

Question 16

In a decision tree for a military attack, the probability of success given heavy showers is 0.12, and the probability of heavy showers is 0.25. What is the probability of a successful attack and heavy showers?

Accepted Answer

$$0.12 	imes 0.25 = 0.03$$

Question 17

Given that the attack was a failure, what is the probability that the weather was heavy showers? (Given $$P(	ext{Heavy showers} | 	ext{Failure}) = 0.11)$$

Accepted Answer

0.11

Statistics Midterm 2 Review: Probability, Sampling, Regression, and Applications

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