Q: Suppose the probability of success in a binomial experiment is $$p = 0.4$$ and $$n = 20. $$What is the standard deviation of the number of successes?

$$\sqrt{np(1-p)} = \sqrt{20 \times 0.4 \times 0.6} \approx 2.19$$

Question 1

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

Accepted Answer

The mean, median, and mode are exactly the same.

Question 2

Suppose the heights of adult women are normally distributed with a mean of $$165 cm $$and a standard deviation of $$6 cm. $$What is the $$z-$$score for a woman who is $$177 cm $$tall?

Accepted Answer

$$z = \frac{177 - 165}{6} = 2$$

Question 3

A probability distribution for a discrete random variable must satisfy which of the following conditions?

Accepted Answer

The sum of all probabilities must equal $$1.$$

Question 4

Which of the following is NOT a condition for a binomial probability model?

Accepted Answer

The probability of success changes from trial to trial.

Question 5

If $$X is a $$binomial random variable with $$n = 10$$ and $$p = 0.3$$, what is the expected value (mean) of $$X$$?

Accepted Answer

$$np = 10 	imes 0.3 = 3$$

Question 6

A continuous random variable $$X$$ has a probability density function (pdf) $$f(x)$$ such that the area under the curve between $$a$$ and $$b$$ represents:

Accepted Answer

The probability that $$X$$ falls between $$a$$ and $$b.$$

Question 7

Given a standard normal distribution, what is the probability that $$Z \u003c 1.25$$? (Use the $$z-$$table approximation.)

Accepted Answer

$$0.8944 ($$from $$z-$$table for $$z = 1.25)$$

Question 8

Which of the following best describes a discrete random variable?

Accepted Answer

The number of heads in 10 coin tosses.

Question 9

Suppose the probability of success in a binomial experiment is $$p = 0.4$$ and $$n = 20. $$What is the standard deviation of the number of successes?

Accepted Answer

$$\sqrt{np(1-p)} = \sqrt{20 	imes 0.4 	imes 0.6} \approx 2.19$$

Question 10

A fair die is rolled. What is the probability of rolling a number less than $$5$$?

Accepted Answer

$$\frac{4}{6} = 0.6667$$

Question 11

Which of the following statements about the standard normal model is correct?

Accepted Answer

It has a mean of $$0$$ and a standard deviation of $$1.$$

Question 12

If the area to the left of $$z = 0.84 in $$the standard normal distribution is $$0.7995$$, what is the probability that $$Z \u003e 0.84$$?

Accepted Answer

$$0.2005$$

Question 13

A hospital records the systolic blood pressure of patients and finds it is approximately normal with mean $$120$$ mmHg and standard deviation $$15$$ mmHg. What is the probability that a randomly selected patient has a systolic blood pressure less than $$135$$ mmHg?

Accepted Answer

Find $$z = \frac{135 - 120}{15} = 1. $$From the $$z-$$table, $$P(Z \u003c 1) = 0.8413.$$

Question 14

Which of the following is a key difference between discrete and continuous random variables?

Accepted Answer

Discrete random variables have countable outcomes; continuous random variables have uncountable outcomes.

Question 15

A binomial distribution can be approximated by a normal distribution when:

Accepted Answer

Both $$np$$ and $$n(1-p)$$ are at least $$15.$$

Question 16

If $$X is a $$continuous random variable with probability density function $$f(x)$$, what is $$P(X = a)$$ for any specific value $$a$$?

Accepted Answer

$$0$$

Question 17

A researcher wants to find the $$90th $$percentile of a normal distribution with mean $$100$$ and standard deviation $$15. $$What $$z-$$score should she use?

Accepted Answer

$$z = 1.28$$

Question 18

Which of the following is NOT a characteristic of a binomial probability model?

Accepted Answer

The number of trials can change during the experiment.

Question 19

Suppose the probability of a randomly selected Canadian having a secondary education is $$0.65. If a $$random sample of $$5$$ Canadians is selected, what is the probability that exactly $$3$$ have a secondary education?

Accepted Answer

$$P(X = 3) = {5 \choose 3} (0.65)^3$ (0.35)^2$ = 0.325$$

Chapter 6

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