Question 1

In a summary of recent real estate sales, the median home price is given as $325,000. What percentile corresponds to a home price of $325,000?

Accepted Answer

The answer of In a summary of recent real estate...

Question 2

If a sample has mean 0 and standard deviation 1, then for every measurement x in the sample the z-score of x is x itself.

Accepted Answer

The z-score is calculated as $z = \frac{x - \mu}{\sigma}$, where $x$ is a measurement, $\mu$ is the mean, and $\sigma$ is the standard deviation. If $\mu = 0$ and $\sigma = 1$, then $z = \frac{x - 0}{1} = x$.

Question 3

A radio station claims that the amount of advertising each hour has a mean of 16 minutes and a standard deviation of 2.7 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 8 minutes. Calculate the z-score for this amount of advertising time.
A) z = -2.96
B) z = 2.96
C) z = -21.6
D) z = 0.33

Accepted Answer

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Here, z = (8 - 16) / 2.7 = -2.96.

Question 4

The mean of a data set is at the 50th percentile.

Accepted Answer

The mean of a data set is the average value, which does not necessarily correspond to the 50th percentile. The 50th percentile, also known as the median, is the value that divides the data set into two equal halves, and it can be different from the mean, especially in skewed distributions.

Question 5

Summary information is given for the weights (in pounds) of 1000 randomly sampled tractor trailers. $$\begin{array} { l r l r } 
\text { MIN: } & 4015 & 25 \% : & 5615 \
\text { MAX: } & 10,615 & 75 \% : & 8615 \
\text { AVE: } & 7015 & \text { Std. Dev.: } & 1400
\end{array}$$ Find the percentage of tractor trailers with weights between 5615 and 8615 pounds.
A) 50%
B) 75%
C) 25%
D) 100%

Accepted Answer

The weights between 5615 and 8615 pounds represent the interquartile range (IQR), which contains the middle 50% of the data.

Question 6

A retail store's customer satisfaction rating is at the 88th percentile. What percentage of retail stores has higher customer satisfaction ratings than this store?

Accepted Answer

The answer of A retail store's customer satisfaction rating is...

Question 7

Suppose that 50 and 75 are two elements of a population data set and their z-scores are -3 and 2, respectively. Find the mean and standard deviation.

Accepted Answer

The answer of Suppose that 50 and 75 are two...

Question 8

A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $142.00 and a standard deviation of $15.00. Assuming the distribution is mound-shaped and symmetric, would you expect to see a 3-bedroom house using gas or electric energy with a monthly utility bill of $239.50? Explain.

Accepted Answer

The answer of A recent survey was conducted to compare...

Question 9

The test scores of 30 students are listed below. Which number could be the 30th percentile? $\begin{array} { l l l l l l l l l l } 31 & 41 & 45 & 48 & 52 & 55 & 56 & 56 & 63 & 65 \end{array}$
$\begin{array} { l l l l l l l l l l } 67 & 67 & 69 & 70 & 70 & 74 & 75 & 78 & 79 & 79 \end{array}$
$\begin{array} { l l l l l l l l l l } 80 & 81 & 83 & 85 & 85 & 87 & 90 & 92 & 95 & 99 \end{array}$
A) 64
B) 56
C) 67
D) 90

Accepted Answer

The answer of The test scores of 30 students are...

Question 10

A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 380 and a standard deviation of 50 on a standardized test. Find and interpret the z-score of a student who scored 450 on the standardized test.

Accepted Answer

The answer of A study was designed to investigate the...

Question 11

Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a mean of 69 with a standard deviation of 3.7. One student earned a 86 on the history test and a 85 on the physics test. Calculate the z-score for each test. On which test did the student perform better?

Accepted Answer

The answer of Test scores for a history class had...

Question 12

The z-score for a value x is -2.5. State whether the value of x lies above or below the mean and by how many standard deviations.

Accepted Answer

The answer of The z-score for a value x is...

Question 13

On a given day, the price of a gallon of milk had a mean price of $2.30 with a standard deviation of $0.05. A particular food store sold milk for $2.25/gallon. Interpret the z-score for this gas station.
A) The milk price of this food store falls 1 standard deviation below the milk gas price of all food stores.
B) The milk price of this food store falls 1 standard deviation above the mean milk price of all food stores.
C) The milk price of this food store falls 5 standard deviations below the mean milk price of all food stores.
D) The milk price of this food store falls 5 standard deviations above the mean milk price of all food stores.

Accepted Answer

The z-score for the food store is (2.25 - 2.30) / 0.05 = -1. This means that the milk price of this food store falls 1 standard deviation below the mean milk price of all food stores.

Question 14

Find the z-score for the value 100, when the mean is 69 and the standard deviation is 5.
A) z = 6.20
B) z = 6.00
C) z = -1.38
D) z = 1.38

Accepted Answer

The answer of Find the z-score for the value 100,...

Question 15

If a z-score is 0 or near 0, the measurement is located at or near the mean.

Accepted Answer

A z-score of 0 represents the mean. Therefore, if a z-score is 0 or near 0, the measurement is located at or near the mean.

Question 16

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?
A) The average of the 500 textbook costs was $500.
B) 75% of the students sampled had textbook costs that exceeded $500.
C) 75% of the students sampled had textbook costs equal to $500.
D) 25% of the students sampled had textbook costs that exceeded $500.

Accepted Answer

The 75th percentile means that 75% of the students had textbook costs less than or equal to $500, so 25% had costs that exceeded $500.

Question 17

According to the empirical rule, z-scores of less than -3 or greater than 3 occur very infrequently for data from a mounded and symmetric distribution

Accepted Answer

The empirical rule states that for data from a mounded and symmetric distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. This suggests that z-scores of less than -3 or greater than 3 occur very infrequently.

Question 18

Which of the following is a measure of relative standing?
A) z-score
B) mean
C) variance
D) pie chart

Accepted Answer

A z-score is a measure of relative standing that indicates how many standard deviations a data point is above or below the mean.

Question 19

The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. $$\begin{array} { l l l l l l l l l l } 
39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \
71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \
79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \
85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \
90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98
\end{array}$$ Find the z-scores for the highest and lowest exam scores.

Accepted Answer

The answer of The following data represent the scores of...

Question 20

When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 67th percentile on the verbal part of the test and at the 38th percentile on the quantitative part. Interpret these results.
A) This student performed better than 67% of the other test-takers on the verbal part and better than 38% on the quantitative part.
B) This student performed better than 67% of the other test-takers on the verbal part and better than 62% on the quantitative part.
C) This student performed better than 33% of the other test-takers on the verbal part and better than 62% on the quantitative part.
D) This student performed better than 33% of the other test-takers on the verbal part and better than 38% on the quantitative part.

Accepted Answer

Percentiles indicate the percentage of scores that fall below a particular score. Scoring at the 67th percentile means the student performed better than 67% of test-takers on the verbal part, and scoring at the 38th percentile means they performed better than 38% on the quantitative part.

Quiz 2: Methods for Describing Sets of Data

In a summary of recent real estate sales, the median home price is given as $325,000. What percentile corresponds to a home price of $325,000?

If a sample has mean 0 and standard deviation 1, then for every measurement x in the sample the z-score of x is x itself.

A radio station claims that the amount of advertising each hour has a mean of 16 minutes and a standard deviation of 2.7 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 8 minutes. Calculate the z-score for this amount of advertising time.

The mean of a data set is at the 50th percentile.

A retail store's customer satisfaction rating is at the 88th percentile. What percentage of retail stores has higher customer satisfaction ratings than this store?

Suppose that 50 and 75 are two elements of a population data set and their z-scores are -3 and 2, respectively. Find the mean and standard deviation.

The z-score for a value x is -2.5. State whether the value of x lies above or below the mean and by how many standard deviations.

On a given day, the price of a gallon of milk had a mean price of $2.30 with a standard deviation of $0.05. A particular food store sold milk for $2.25/gallon. Interpret the z-score for this gas station.

Find the z-score for the value 100, when the mean is 69 and the standard deviation is 5.

If a z-score is 0 or near 0, the measurement is located at or near the mean.

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?

According to the empirical rule, z-scores of less than -3 or greater than 3 occur very infrequently for data from a mounded and symmetric distribution

Which of the following is a measure of relative standing?

When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 67th percentile on the verbal part of the test and at the 38th percentile on the quantitative part. Interpret these results.