Question

A set of data with a normal distribution has a mean of 35 and standard deviation of 5.

a. 68% of the data is between what two numbers?
b. 95% of the data is between what two numbers?
c. About what percent of the population (data) is above 40?

Answer 1

a. 68% of the data is between 30 and 40. b. 95% of the data is between 25 and 45. c. About 16% of the population is above 40.

Step-by-step explanation:

a. 68% of the data is between 1 standard deviation below the mean and 1 standard deviation above the mean. In this case, 1 standard deviation is equal to 5, so the range would be from 35 - 5 = 30 to 35 + 5 = 40.

b. 95% of the data is between 2 standard deviations below the mean and 2 standard deviations above the mean. In this case, 2 standard deviations is equal to 10, so the range would be from 35 - 10 = 25 to 35 + 10 = 45.

c. To find the percentage of the population (data) above 40, we can use the z-score formula. The z-score is the number of standard deviations a value is away from the mean. In this case, the z-score for 40 would be (40 - 35) / 5 = 1. We can then use a standard normal distribution table to find the percentage associated with a z-score of 1, which is approximately 84%. Therefore, about 84% of the population is below 40, so about 16% of the population is above 40.