Question 1

A population of women aged 18-24 has a mean systolic blood pressure of $$\mu = 114.8 mm Hg $$and a standard deviation of $$\sigma = 13.1 mm Hg. $$What is the probability that a randomly selected woman from this population has a systolic blood pressure greater than 120 mm Hg?

Accepted Answer

$$0.3946$$

Question 2

Given the same population as above, if a random sample of 40 women is selected, what is the probability that their mean systolic blood pressure is greater than 120 mm Hg?

Accepted Answer

$$0.0060$$

Question 3

A normal distribution has a mean $$\mu = 560$$ and standard deviation $$\sigma = 85. $$What value $$x$$ corresponds to the 90th percentile?

Accepted Answer

$$668.8$$

Question 4

A table shows that out of 226 people, 89 are male smokers. What is the probability that a randomly selected individual is a male smoker?

Accepted Answer

$$0.3938$$

Question 5

Given a table of 226 people, 204 are non-smokers and 99 are female. What is the probability that a randomly selected individual is either a non-smoker or a female?

Accepted Answer

$$0.849$$

Question 6

Suppose two cards are drawn from a standard deck of 52 playing cards without replacement. What is the probability that both cards are face cards?

Accepted Answer

$$0.0498$$

Question 7

Given the following probability distribution for a discrete random variable $$X$$:

$$\begin{align*}
X & : 0 \quad 1 \quad 2 \quad 4 \
P(X) & : 0.40 \quad 0.31 \quad 0.23 \quad 0.02
\end{align*}$$

What is the mean $$\mu of$$ $$X$$? (Round to two decimal places.)

Accepted Answer

$$0.97$$

Question 8

A binomial experiment has $$n = 10$$ trials and probability of success $$p = 0.6. $$What is the probability of exactly 8 successes?

Accepted Answer

$$0.1209$$

Question 9

In a normal distribution, what is the $$z-$$score for a value $$x = 120$$ given $$\mu = 114.8$$ and $$\sigma = 13.1$$?

Accepted Answer

$$0.40$$

Question 10

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 11

A sample of 226 people is classified by smoking status and gender. If 84 are male non-smokers, what is the probability that a randomly selected person is a male non-smoker?

Accepted Answer

$$0.204$$

Question 12

If the mean of a normal distribution is $$\mu = 560$$ and the standard deviation is $$\sigma = 85$$, what is the $$z-$$score for $$x = 668.8$$?

Accepted Answer

$$1.28$$

Question 13

If $$P(A) = 0.6$$ and $$P(B) = 0.4$$ and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.24$$

Question 14

A deck of 52 cards contains 12 face cards. If two cards are drawn without replacement, what is the probability that the first card is a face card and the second card is not?

Accepted Answer

$$0.1977$$

Question 15

Given a binomial distribution with $$n = 10$$ and $$p = 0.6$$, what is the expected value $$E(X)$$?

Accepted Answer

$$6$$

Question 16

If $$P(A|B) = 0.8990$$ and $$P(B) = 0.3938$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.3539$$

Question 17

A discrete random variable $$X$$ has the following probability distribution:

$$\begin{align*}
X & : 0 \quad 1 \quad 2 \quad 4 \
P(X) & : 0.40 \quad 0.31 \quad 0.23 \quad 0.02
\end{align*}$$

What is the probability that $$X \geq 2$$?

Accepted Answer

$$0.25$$

Question 18

If the probability that a randomly selected person is a non-smoker is $$0.849$$, what is the probability that a randomly selected person is a smoker?

Accepted Answer

$$0.151$$

Question 19

A normal distribution has $$\mu = 114.8$$ and $$\sigma = 13.1. $$What is the probability that a randomly selected value is less than $$x = 120$$?

Accepted Answer

$$0.6554$$

Question 20

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Probability, Normal Distributions, and Discrete Random Variables: Study Notes

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