Q: A baseball player has a batting average of 0.308 and bats 480 times in a season. What is the expected number of hits?

$$\mu = 480 \times 0.308 = 147.84$$

Q: If the final exam scores are normally distributed with a mean of 95 and a standard deviation of 18, what score differentiates the lower 20% (F) from the rest?

$$z = -0.84$$, so score = $$95 + (-0.84) \times 18 = 79.88$$

Question 1

Which of the following is a discrete random variable?

Accepted Answer

The number of cars owned by a household

Question 2

A random variable $$X is $$defined as the number of heads in 3 coin tosses. What type of random variable is $$X$$?

Accepted Answer

Discrete random variable

Question 3

Which requirement is NOT necessary for a binomial model?

Accepted Answer

The number of successes must be greater than the number of failures

Question 4

Suppose $$X \sim B(5, 0.4). $$What is the expected value (mean) of $$X$$?

Accepted Answer

$$\mu = 2$$

Question 5

For a binomial distribution $$X \sim B(n, p)$$, what is the formula for the standard deviation?

Accepted Answer

$$\sigma = \sqrt{np(1-p)}$$

Question 6

A die is rolled once. What is the probability of rolling a 3?

Accepted Answer

$$\frac{1}{6}$$

Question 7

According to the Empirical Rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 8

Suppose the weights of students at a school are normally distributed with a mean of 140 lbs and a standard deviation of 6 lbs. What is the z-score for a student weighing 152 lbs?

Accepted Answer

$$z = 2$$

Question 9

A radar unit measures the speed of cars on a highway, which is normally distributed with a mean of 80 mph and a standard deviation of 15 mph. What is the probability that a car is traveling more than 110 mph?

Accepted Answer

$$P(X \u003e 110) = P(Z \u003e 2) \approx 0.0228$$

Question 10

If SAT scores are distributed as $$X \sim N(1010, 20)$$, what is the z-score for a student who scored 1050?

Accepted Answer

$$z = 2$$

Question 11

In a binomial experiment with $$n = 25$$ and $$p = 0.84$$, what is the expected number of people who use a seat belt?

Accepted Answer

$$\mu = 21$$

Question 12

For a continuous probability distribution, which statement is TRUE?

Accepted Answer

The probability of a single value is zero

Question 13

Suppose the minimum daily temperature in New York City in February is normally distributed with a mean of 27°F and a standard deviation of 6°F. What percentage of days in February has a minimum temperature below freezing (32°F)?

Accepted Answer

About 84%

Question 14

If $$X \sim N(125, 10)$$ represents systolic blood pressure, what percentage of females have blood pressure between 115 and 135 mmHg?

Accepted Answer

68%

Question 15

A baseball player has a batting average of 0.308 and bats 480 times in a season. What is the expected number of hits?

Accepted Answer

$$\mu = 480 	imes 0.308 = 147.84$$

Question 16

For a standard normal distribution $$Z \sim N(0,1)$$, what is the probability that $$Z \u003e 1.35$$?

Accepted Answer

$$P(Z \u003e 1.35) \approx 0.0885$$

Question 17

Suppose you randomly sample 30 students and count the number who are female, where 57% of students are female. What is the correct binomial model for this scenario?

Accepted Answer

$$X \sim B(30, 0.57)$$

Question 18

If the final exam scores are normally distributed with a mean of 95 and a standard deviation of 18, what score differentiates the lower 20% (F) from the rest?

Accepted Answer

$$z = -0.84$$, so score = $$95 + (-0.84) 	imes 18 = 79.88$$

Question 19

Which of the following is NOT a requirement for a binomial distribution?

Accepted Answer

Each trial can have more than two outcomes

Chapter 6: Modeling Random Events – The Normal and Binomial Models

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