1. Arturo’s Restaurant has a mean rating of 8.0 with a standard deviation of .8. Tony’s Restaurant: also has a mean rating by customers of 8.0, but with a standard deviation of 1.2.At which restaurant is the service likely to be more variable?
a. Arturo’s. The lower standard deviation indicates greater variability.
b. Tony's. The higher standard deviation indicates greater variability.
2.A student scored 148 on a recent exam that had a mean of 180 and standard deviation of 15. Which of the following is the most accurate interpretation?
a. This is not good, because the student was more than 2 standard deviations below the mean.
b.. This is good, because the student was more than 2 standard deviations below the mean.
c. This is good, because the student was more than 2 standard deviations above the mean.
d. This is not good, because the student was more than 2 standard deviations above the mean.
2 is A
1. The correct answer is b. Tony's. The higher standard deviation indicates greater variability.
2. The correct answer is a. This is not good, because the student was more than 2 standard deviations below the mean. Since the student scored 148, which is more than 2 standard deviations (15 x 2 = 30) below the mean of 180, it indicates a below-average performance.
1. To determine which restaurant is likely to have more variable service, we need to compare their standard deviations. The standard deviation measures the spread of the data points from the mean.
For Arturo's Restaurant, the standard deviation is 0.8, while for Tony's Restaurant, the standard deviation is 1.2.
The option that correctly determines which restaurant is likely to have more variable service is:
b. Tony's. The higher standard deviation indicates greater variability.
Explanation: A higher standard deviation indicates that the ratings for Tony's Restaurant are more spread out from the mean. This suggests that the service at Tony's is more variable compared to Arturo's, where the ratings are less spread out.
2. To interpret the score of 148 on the exam, we need to compare it to the mean and the standard deviation of the exam scores.
Given:
Mean = 180
Standard Deviation = 15
The option that provides the most accurate interpretation is:
a. This is not good, because the student was more than 2 standard deviations below the mean.
Explanation: To determine how significant a score is, we can calculate the number of standard deviations it is away from the mean. In this case, the student's score of 148 is 32 points below the mean (180 - 148 = 32). Since the standard deviation is 15, the number of standard deviations below the mean is 32 / 15 = 2.13 (approximately).
Since the student's score is more than 2 standard deviations below the mean, it indicates that the student's performance is below average, suggesting that it is not a good result. Therefore, option a is the most accurate interpretation.