Q: Given the frequency table of pulse rates for females, estimate the mean pulse rate. Use the class midpoint method.

$$\frac{(64.5 \times 12) + (74.5 \times 14) + (84.5 \times 11) + (94.5 \times 1) + (104.5 \times 1) + (114.5 \times 0) + (124.5 \times 1)}{40}$$

Q: A student’s project grade is weighted: 30% first essay, 25% presentation, 45% final essay. If Lewis scored 88 on the first essay and 100 on the presentation, what must they score on the final essay to have a weighted average of 90? (Round up to the nearest whole number.)

$$\lceil \frac{90 - (0.3 \times 88 + 0.25 \times 100)}{0.45} \rceil = 86$$

Q: A different soda can has a z-score of -1.33. The mean is 11.98 ounces and the standard deviation is 0.03 ounces. What is the volume of this can?

$$x = 11.98 + (-1.33 \times 0.03) = 11.94$$

Q: A bag contains 20 marbles: 4 red, 6 green, 7 blue, and 3 white. If two marbles are drawn without replacement, what is the probability that both are green?

$$\frac{6}{20} \times \frac{5}{19} = \frac{30}{380} = 0.079$$

Question 1

Given the frequency table of pulse rates for females, estimate the mean pulse rate. Use the class midpoint method.

Accepted Answer

$$\frac{(64.5 	imes 12) + (74.5 	imes 14) + (84.5 	imes 11) + (94.5 	imes 1) + (104.5 	imes 1) + (114.5 	imes 0) + (124.5 	imes 1)}{40}$$

Question 2

In which class interval will the median pulse rate be found, based on the frequency table?

Accepted Answer

80-89

Question 3

A trivia game has scores that are approximately normally distributed with a mean of 18 and a standard deviation of 3. What percentage of people would be expected to score between 15 and 21 points?

Accepted Answer

About 68%

Question 4

For the same trivia game, what percentage of people would be expected to score between 9 and 27 points?

Accepted Answer

About 95%

Question 5

Given the population data points: 35, 35, 20, 50, 30. What is the mean?

Accepted Answer

$$\frac{35 + 35 + 20 + 50 + 30}{5} = 34$$

Question 6

Given the same data set (35, 35, 20, 50, 30), what is the median?

Accepted Answer

35

Question 7

A student’s project grade is weighted: 30% first essay, 25% presentation, 45% final essay. If Lewis scored 88 on the first essay and 100 on the presentation, what must they score on the final essay to have a weighted average of 90? (Round up to the nearest whole number.)

Accepted Answer

$$\lceil \frac{90 - (0.3 	imes 88 + 0.25 	imes 100)}{0.45} ceil = 86$$

Question 8

If the standard deviation is 3.7 m, what is the variance?

Accepted Answer

$$3.7^2 = 13.69$

Question 9

If the variance is 221.8 $$cm^6$$, what is the standard deviation?

Accepted Answer

$$\sqrt{221.8} = 14.9$$

Question 10

A soda can has a volume of 12.10 ounces. The average is 11.98 ounces and the standard deviation is 0.03 ounces. What is the z-score for this can?

Accepted Answer

$$z = \frac{12.10 - 11.98}{0.03} = 4.00$$

Question 11

A different soda can has a z-score of -1.33. The mean is 11.98 ounces and the standard deviation is 0.03 ounces. What is the volume of this can?

Accepted Answer

$$x = 11.98 + (-1.33 	imes 0.03) = 11.94$$

Question 12

A quiz has three questions: the first is True/False, the second has 4 choices (A/B/C/D), and the third is Yes/No/Maybe. How many possible simple events (response sets) are possible?

Accepted Answer

$$2 	imes 4 	imes 3 = 24$$

Question 13

A fair coin is tossed four times. What is the probability of getting exactly 2 heads and 2 tails?

Accepted Answer

$$\frac{6}{16} = 0.375$$

Question 14

A bag contains 20 marbles: 4 red, 6 green, 7 blue, and 3 white. If two marbles are drawn without replacement, what is the probability that both are green?

Accepted Answer

$$\frac{6}{20} 	imes \frac{5}{19} = \frac{30}{380} = 0.079$$

Introductory Statistics Study Guide: Frequency Tables, Normal Distribution, Descriptive Statistics, Probability, and More

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