Question 1

Given the sample of ages $$A = \{23, 27, 17, 24, 31, 38, 29, 42, 21, 19, 20, 33, 32, 22, 21, 23, 20, 25, 20, 21, 24\}$$, what is the z-score for the youngest student in the sample? (Round your answer to two decimal places.)

Accepted Answer

$$z = -2.13$$

Question 2

A jar contains 35 red and 15 black balls. If two balls are drawn with replacement, what is the probability that both balls are red? (Express your answer to three decimal places.)

Accepted Answer

$$p = 0.343$$

Question 3

A sample of five balls is chosen at random without replacement from a jar containing 35 red and 15 black balls. What is the probability that exactly three out of five balls are red? (Express your answer to three decimal places.)

Accepted Answer

$$p = 0.395$$

Question 4

A group of five balls is chosen from a jar with replacement. What is the probability that exactly three of the five balls are red? (Express your answer to three decimal places.)

Accepted Answer

$$p = 0.329$$

Question 5

A researcher claims a strong relationship exists between SAT-Math score and Calculus 1 final exam points. Given the following data for 11 students, what is the Pearson correlation coefficient $$r$$ between SAT-Math and Calculus 1 points? (Round to three decimal places.)

Accepted Answer

$$r = 0.972$$

Question 6

Using the regression line from the previous question, predict the Calculus 1 exam score for a student with an SAT-Math score of 690. (Round to two decimal places.)

Accepted Answer

$$y = 85.23$$

Question 7

IQ scores are normally distributed with mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What proportion of people should score between 85 and 130 on an IQ test? (Express your answer to three decimal places.)

Accepted Answer

$$p = 0.818$$

Question 8

What IQ score corresponds to the 30th percentile? (Round to the nearest whole number.)

Accepted Answer

$$IQ = 94$$

Question 9

Thirty-six percent of students at a college receive Pell Grants. What is the probability that, in a random sample of 30 students, exactly 10 receive Pell Grants? (Express your answer to three decimal places.)

Accepted Answer

$$p = 0.172$$

Question 10

In a college of 10,000 students, the expected number of expulsions for academic dishonesty per semester is 5. What is the probability that exactly 4 students are expelled this semester? (Use the Poisson distribution. Express your answer to three decimal places.)

Accepted Answer

$$p = 0.175$$

Question 11

A sociologist proposes the probability distribution $$P(x) = \frac{28 - 2x^2$}{84}$$ for $$x = 0, 1, 2, 3 ($$number of times a male statistics teacher has been married). What is the mean of this distribution?

Accepted Answer

$$\mu = 0.81$$

Question 12

Given the same probability distribution $$P(x) = \frac{28 - 2x^2$}{84}$$ for $$x = 0, 1, 2, 3$$, what is the probability that a randomly selected teacher has been married less than three times?

Accepted Answer

$$p = 0.952$$

Question 13

It is estimated that 75% of HFC first-semester students have already earned a high school diploma. You randomly select 108 students. Using the normal approximation to the binomial, what is the probability that between 80 and 82 (inclusive) have graduated? (Express your answer to four decimal places.)

Accepted Answer

$$p = 0.2610$$

Question 14

A contingency table of 800 Pizza Hut customers records whether they usually order Italian sausage (S) and/or mushrooms (M) on their pizza. Which of the following probabilities is the greatest?

Accepted Answer

$$P(S 	ext{ or } M)$$

Question 15

The correlation between the number of times a student skipped class and their final exam score is $$r = -0.625. $$What percent of the variation in exam scores is due to factors other than the number of times a student missed class?

Accepted Answer

$$60.9\%$$

Question 16

A research director sends a survey to every twentieth student who enrolled for the Fall 2026 semester. What sampling method, other than random sampling, is being used?

Accepted Answer

Systematic sampling

Question 17

Which of the following best describes the level of measurement for 'age'?

Accepted Answer

Ratio, continuous

Question 18

If a variable is measured at the ratio level, which of the following statements is always true?

Accepted Answer

The variable has a true zero and equal intervals.

Question 19

A college administrator wants to estimate the proportion of students who receive Pell Grants. Which of the following would be the most appropriate probability distribution to model the number of Pell Grant recipients in a random sample of 30 students?

Accepted Answer

Binomial distribution

Question 20

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the z-score for an IQ of 130?

Accepted Answer

$$z = 2.00$$

Step-by-Step Guidance for Statistics Problem Set (MATH141)

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