Question 1

A nurse measured the systolic blood pressure of people aged 25-40 and created a relative-frequency histogram. If the histogram shows that 75% of the readings fall between 110 and 139 inclusive, what does this percentage represent?

Accepted Answer

The proportion of people in the sample with systolic blood pressure in that range.

Question 2

Sam studied for an exam over five days with the following hours: 1.5, 8.3, 6.9, 1.8, 5.3. What is the mean study time, rounded to two decimal places?

Accepted Answer

$$4.76\ 	ext{hr}$$

Question 3

Given the sample data: 47, 55, 71, 41, 82, 57, 25, 66, 81, what is the sample standard deviation? Round your answer to one decimal place.

Accepted Answer

$$20.2$$

Question 4

A manufacturing process has a 70% yield. If three products are randomly selected, what is the probability that all are acceptable? (Assume independence.)

Accepted Answer

$$0.343$$

Question 5

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. What is the probability that the first card is a King and the second card is a Queen?

Accepted Answer

$$4/663$$

Question 6

A sample of 4 calculators is randomly selected from a group of 18 defective and 40 non-defective calculators. What is the probability that at least one is defective? (Round to the nearest thousandth.)

Accepted Answer

$$0.785$$

Question 7

Identify the given random variable as discrete or continuous: The height of a randomly selected student.

Accepted Answer

Continuous

Question 8

Suppose you buy 1 ticket for $$1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is 500. $$What is your expected value?

Accepted Answer

$$-0.50$$

Question 9

Choosing 5 people (without replacement) from a group of 40 people, of which 15 are women, keeping track of the number of men chosen. Does this procedure result in a binomial distribution?

Accepted Answer

Not binomial: the trials are not independent.

Question 10

Assume a binomial distribution with $$n=30$$, $$x=12$$, $$p=0.20. $$Use the binomial probability formula to find $$P(X=12). $$Round to three decimal places.

Accepted Answer

$$0.003$$

Question 11

Find the mean $$\mu$$ for a binomial distribution with $$n=676$$ and $$p=0.7. $$Round to the nearest tenth.

Accepted Answer

$$\mu=473.2$$

Question 12

At one college, GPAs are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students have a GPA between 2.4 and 3.6? (Use the empirical rule.)

Accepted Answer

68%

Question 13

The mean of a set of data is $$108.06$$ and its standard deviation is $$115.45. $$What is the $$z-$$score for a value of $$489.67$$? (Round to the nearest hundredth.)

Accepted Answer

$$z=3.31$$

Question 14

A class consists of 27 women and 32 men. If a student is randomly selected, what is the probability that the student is a woman?

Accepted Answer

$$\dfrac{27}{59}$$

Question 15

What is the sample space for flipping a coin twice?

Accepted Answer

HH, HT, TH, TT

Question 16

A sample of 100 wood and 100 graphite tennis rackets are taken from a warehouse. If 7 wood and 14 graphite are defective, what is the probability that a randomly selected racket is wood or defective?

Accepted Answer

$$0.57$$

Question 17

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 4?

Accepted Answer

$$\dfrac{4}{13}$$

Question 18

A group of asthma sufferers is surveyed about their smoking habits. If the probability of selecting a man or a heavy smoker is $$0.596$$, what does this probability represent?

Accepted Answer

The chance that a randomly selected person from the group is either a man or a heavy smoker.

Question 19

A probability distribution describes the number of adults (among 4 randomly selected) who have a college degree, with $$p=0.7. $$What is the standard deviation $$\sigma of $$this binomial distribution? (Round to the nearest hundredth.)

Accepted Answer

$$\sigma=0.92$$

Question 20

A real-world scenario: In a hospital, 60% of patients recover from a certain treatment. If 5 patients are treated, what is the probability that exactly 3 recover? (Use the binomial formula and round to three decimal places.)

Accepted Answer

$$0.346$$

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