Q: Given the regression equation $$\text{salary} = 2050 + 1300 \times \text{GPA}$$, what is the predicted salary for a student with a GPA of 3.2?

$$2050 + 1300 \times 3.2 = 6210$$

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

6

Question 2

Suppose a random sample contains 60 kids, 25% of whom have a FREE logo under their cap. What is the probability that you find two free caps in a group of 4?

Accepted Answer

$$P(X=2) = \binom{4}{2} (0.25)^2$ (0.75)^2$ = 0.2109$$

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 $$231 with a standard deviation of 48. $$What is the standard deviation of the total monthly spending for 1,120 children, assuming independence?

Accepted Answer

$$\sqrt{62^2$ + 48^2$} = 78.8$$

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?

Accepted Answer

$$1 - (0.57)^5$ = 0.947$$

Question 5

A certain synthetic chemical is known to be toxic at high levels. What is the probability that the average sample mean will be smaller than the true mean if the sample size is large?

Accepted Answer

$$0.5$$

Question 6

The Central Limit Theorem (CLT) only applies to the sampling distribution of means when:

Accepted Answer

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

Question 7

A factory has to randomly inspect its products. To inspect a representative sample of 100 items, which sampling method is most likely to avoid bias?

Accepted Answer

Simple random sampling

Question 8

A researcher wants to compare the performance of three types of pain relievers in volunteers with chronic arthritis. The best experimental design would be:

Accepted Answer

Randomized block design by type of arthritis

Question 9

Given the regression equation $$	ext{salary} = 2050 + 1300 	imes 	ext{GPA}$$, what is the predicted salary for a student with a GPA of 3.2?

Accepted Answer

$$2050 + 1300 	imes 3.2 = 6210$$

Question 10

If a study shows that 35% of traffic accidents involved both alcohol and speeding, and 60% involved alcohol, 50% involved speeding, what is the probability that an accident involved alcohol but not speeding?

Accepted Answer

$$0.60 - 0.35 = 0.25$$

Question 11

A fast food restaurant just issued a new service contract for three years. The service contract for the kitchen equipment requires a fee of $$125 a year plus a 25 $$service charge for each repair. If the expected number of repairs per year is 3, what is the expected annual cost?

Accepted Answer

$$125 + 3 	imes 25 = 200$$

Question 12

If the number of repairs per year is Poisson with mean $$\lambda = 3$$, what is the expected number of repairs in three consecutive years?

Accepted Answer

$$3 	imes 3 = 9$$

Question 13

The American Red Cross says that about 15% of the U.S. population has Type B blood. What is the probability that exactly 3 of the first 20 blood donors at a blood drive have Type B blood?

Accepted Answer

$$P(X=3) = \binom{20}{3} (0.15)^3$ (0.85$$)^{17}$$

Question 14

What is the probability that at least 2 of the first 20 blood donors at the blood drive have Type B blood?

Accepted Answer

$$1 - P(X=0) - P(X=1)$$

Question 15

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

Accepted Answer

$$P(\bar{X} \u003e 13.2) = P\left(Z \u003e \frac{13.2 - 13}{0.3/\sqrt{12}}\right)$$

Question 16

Suppose you are given the following probabilities: $$P(	ext{Heavy shower} | 	ext{Failure}) = 0.12$$, $$P(	ext{Light shower} | 	ext{Failure}) = 0.25$$, $$P(	ext{No shower} | 	ext{Failure}) = 0.63. $$What is the probability of a heavy shower given a failure?

Accepted Answer

$$0.12$$

Question 17

If two risk factors are dependent, which of the following must be true?

Accepted Answer

$$P(A \cap B) 
eq P(A)P(B)$$

Question 18

If the distribution of cereal box weights is approximately Normal, and the Central Limit Theorem applies, what is the standard deviation of the sample mean for samples of size $$n$$?

Accepted Answer

$$\sigma / \sqrt{n}$$

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

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