Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in the table below. What is the Relative Frequency for flossing 1 time per week?

Question

# flossing per week

Frequency

Relative Frequency

0

27

0.4500

1

18



3

11



6

3

0.0500

7

1

0.0167

Question 1 options:

0.75

18

0.45

0.3

Question 2 (1 point)

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Because of the existence of extremely wealthy individuals, economic data concerning income is very skewed. Which statement regarding the distribution of income is correct?

Question 2 options:

Due to the skew the median will be a better measure of center for this data than the mean

The standard deviation will be a good measure of spread for this data.

Each section of a boxplot will be about the same width.

Due to the skew the median is greater than the mean.

Question 3 (1 point)

230 students taking MATH 1001 or MATH 1111 were organized by their math class and gender in the following contingency chart. Use the table to find the requested probability.



Male

Female

Total

1001

52

78

130

1111

63

37

100

Total

115

115

230

If one student is randomly selected, what is the probability that they are male and in 1001?

Question 3 options:

52/115

52/130

130/230

52/230

Question 4 (1 point)

230 students taking MATH 1001 or MATH 1111 were organized by their math class and gender in the following contingency chart. Use the table to find the requested probability.



Male

Female

Total

1001

52

78

130

1111

63

37

100

Total

115

115

230

If one random student is selected, what is the probability that they are male given they are in 1001?

Question 4 options:

52/115

52/130

130/230

52/230

Question 5 (1 point)

The mean height of women on Division I basketball teams is 71.4 inches with a standard deviation of 4.2 inches. Kylee plays Division I basketball and has a height of 73.5 inches. How many standard deviations above or below the mean height is Kylee?

Question 5 options:

0.5 above

0.5 below

2.1 above

2.1 below

Answer 1

Let's solve each question step by step.

Question 1

We need to calculate the relative frequency for flossing 1 time per week.

The formula for relative frequency is: \[ \text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Frequency}} \]

Total frequency of flossing is calculated from the frequencies in the table:

• 0 times: 27
• 1 time: 18
• 3 times: 11
• 6 times: 3
• 7 times: 1

Total Frequency = 27 + 18 + 11 + 3 + 1 = 60

Now calculating the relative frequency for flossing 1 time per week: \[ \text{Relative Frequency for 1 time} = \frac{18}{60} = 0.3 \]

Answer: 0.3

Question 2

Given the skew in income data due to extremely wealthy individuals, the distribution is likely right-skewed. In such cases:

• The median is less affected by outliers compared to the mean, making it a better measure of center.

Thus, the correct statement is: Due to the skew the median will be a better measure of center for this data than the mean.

Answer: Due to the skew the median will be a better measure of center for this data than the mean.

Question 3

We need to find the probability that a randomly selected student is male and in MATH 1001.

From the table:

• Number of males in 1001: 52
• Total students: 230

Thus, the probability is: \[ P(\text{Male and in 1001}) = \frac{52}{230} \]

Answer: 52/230

Question 4

We need to find the conditional probability that a student is male given that they are in MATH 1001.

From the table, total students in MATH 1001 is 130 (52 males + 78 females). The number of males in 1001 is 52.

Thus, the probability is: \[ P(\text{Male | in 1001}) = \frac{52}{130} \]

Answer: 52/130

Question 5

To find how many standard deviations Kylee’s height is above or below the mean, we use the z-score formula: \[ z = \frac{(X - \mu)}{\sigma} \] Where:

• \(X\) is Kylee’s height (73.5 inches),
• \(\mu\) is the mean height (71.4 inches),
• \(\sigma\) is the standard deviation (4.2 inches).

Calculating the z-score: \[ z = \frac{(73.5 - 71.4)}{4.2} = \frac{2.1}{4.2} = 0.5 \]

Since Kylee’s height is above the mean: Answer: 0.5 above

Putting it all together:

• Question 1: 0.3
• Question 2: Due to the skew the median will be a better measure of center for this data than the mean.
• Question 3: 52/230
• Question 4: 52/130
• Question 5: 0.5 above