Question 1

Suppose the heights of adult men are approximately Normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the z-score for a man who is 76 inches tall?

Accepted Answer

$$z = \frac{76 - 70}{3} = 2$$

Question 2

A company claims its batteries last an average of 100 hours with a standard deviation of 10 hours. According to the 68-95-99.7 Rule, what percentage of batteries should last between 90 and 110 hours?

Accepted Answer

About 68%

Question 3

If SAT scores are Normally distributed with mean 500 and standard deviation 100, what is the approximate percentile rank of a score of 600?

Accepted Answer

84th percentile

Question 4

A tire company finds that the tread life of its snow tires is Normally distributed with mean 32,000 miles and standard deviation 2,500 miles. What is the probability that a randomly selected tire lasts more than 40,000 miles?

Accepted Answer

About 0.7%

Question 5

A college admits only students with SAT scores in the top 10%. If SAT scores are $$N(500, 100)$$, what is the minimum SAT score required for admission?

Accepted Answer

630

Question 6

If $$X \sim N(10, 2)$$ and $$Y \sim N(15, 3)$$ are independent, what is the distribution of $$X + Y$$?

Accepted Answer

$$N(25, \sqrt{13})$$

Question 7

A manufacturer wants to guarantee a minimum tread life to no more than 1 out of 25 customers. If tread life is $$N(32,000, 2,500)$$, what is the lowest mileage he should guarantee?

Accepted Answer

27,000 miles

Question 8

Which of the following is NOT a condition for using the Normal approximation to the Binomial distribution?

Accepted Answer

The probability of success must be close to 0.5.

Question 9

Suppose you wait for a bus that arrives every 20 minutes, and the wait time is uniformly distributed between 0 and 20 minutes. What is the mean wait time?

Accepted Answer

$$\frac{0 + 20}{2} = 10$$ minutes

Question 10

A Normal probability plot of a dataset shows a strong curve rather than a straight line. What does this indicate?

Accepted Answer

The data are not Normally distributed.

Question 11

If $$X \sim N(100, 15)$$, what is the probability that $$X is $$between 85 and 115?

Accepted Answer

About 68%

Question 12

A cereal company finds the probability of finding a prize in a box is 0.2. If you open 50 boxes, what is the mean and standard deviation of the number of prizes found?

Accepted Answer

Mean: $$np = 10$$, SD: $$\sqrt{np(1-p)} = 2.83$$

Question 13

Which of the following best describes the 68-95-99.7 Rule for a Normal distribution?

Accepted Answer

About 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD of the mean

Question 14

If the sum of two independent Normal random variables $$X \sim N(5, 2)$$ and $$Y \sim N(7, 3) is$$ $$Z = X + Y$$, what is the variance of $$Z$$?

Accepted Answer

$$2^2$$ + $$3^2 = 13$

Question 15

Which of the following is a property of the Normal distribution?

Accepted Answer

It is symmetric and bell-shaped.

Question 16

If a value has a z-score of 2.5 in a Normal distribution, what does this mean?

Accepted Answer

The value is 2.5 standard deviations above the mean.

Question 17

Which of the following is the probability density function for a uniform distribution on $$[a, b]$$?

Accepted Answer

$$f(x) = \frac{1}{b-a}$$ for $$a \leq x \leq b$$

The Normal and Other Continuous Distributions: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드