Question 1

A study reports that systolic blood pressure for women aged 18-24 is normally distributed with mean $$\mu = 114.8 mm Hg $$and standard deviation $$\sigma = 13.1 mm Hg. $$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

If 40 women are randomly selected from the same population (mean $$\mu = 114.8$$, $$\sigma = 13.1$$), what is the probability that their mean systolic blood pressure is greater than 120 mm Hg?

Accepted Answer

$$0.0060$$

Question 3

Given a normal distribution with 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

From the same table, what is the probability of randomly selecting an individual who is not a smoker and is male?

Accepted Answer

$$0.3890$$

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 discrete probability distribution: $$P(0) = 0.40$$, $$P(1) = 0.31$$, $$P(2) = 0.23$$, $$P(4) = 0.02$$, $$P(5) = 0.04$$, what is the mean $$\mu of $$the distribution (rounded 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 $$x = 120 if$$ $$\mu = 114.8$$ 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 independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.20$$

Question 11

A random variable $$X$$ has the following probability distribution: $$P(X=0)=0.40$$, $$P(X=1)=0.31$$, $$P(X=2)=0.23$$, $$P(X=4)=0.02$$, $$P(X=5)=0.04. $$What is the probability that $$X \geq 2$$?

Accepted Answer

$$0.29$$

Question 12

If the probability of an event is $$0.10$$, what is the $$z-$$score that corresponds to the 90th percentile in a standard normal distribution?

Accepted Answer

$$1.28$$

Question 13

A sample of 226 people includes 127 females and 99 males. If 49 males are smokers, what is the probability that a randomly selected male is a smoker?

Accepted Answer

$$0.4949$$

Question 14

If $$P(A) = 0.6$$ and $$P(B|A) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.3$$

Question 15

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

$$0.2045$$

Question 16

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

Accepted Answer

$$6$$

Question 17

If the mean of a normal distribution is $$\mu = 560$$ and the standard deviation is $$\sigma = 85$$, what is the probability that a randomly selected value is less than $$668.8$$?

Accepted Answer

$$0.90$$

Question 18

A probability distribution is given by $$P(0) = 0.40$$, $$P(1) = 0.31$$, $$P(2) = 0.23$$, $$P(4) = 0.02$$, $$P(5) = 0.04. $$What is the variance $$\$$sigma^2$$ of this distribution (rounded to two decimal places)?

Accepted Answer

$$1.13$$

Question 19

If the probability of drawing a face card from a standard deck is $$\frac{12}{52}$$, what is the probability of not drawing a face card in a single draw?

Accepted Answer

$$0.7692$$

Question 20

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cup B) = 0.7$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.2$$

Probability and Statistics: Normal Distribution, Binomial Probability, and Discrete Distributions

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