A set of data has a normal distribution with a mean of 29 and a standard deviation of 4. Find the percent of data within each interval.

27. from 25 to 33

a. 42%

b. 68%

c. 13%

d. 88%

28. from 21 to 25

a. 28.5%

b. 54.5%

c. 13.5%

d. 15.5%

29. greater than 29

a. 50%

b. 75%

c. 25%

d. 100%

30. less than 21

a. 6.5%

b. 10.5%

c. 1.5%

d. 2.5%

Let x be the population distribution.

p (25 ≤ x ≤ 33) = p ((25 - 29) / 4 ≤ z ≤ (33 - 29) / 4) = p (-1 ≤ z ≤ 1) = p (z ≤ 1) - p (z ≤ - 1) = p (z ≤ 1) - [1 - p (z ≤ 1) ] = 2p (z ≤ 1) - 1 = 2 (0.84134) - 1 = 0.68268 = 68%

p (21 ≤ x ≤ 25) = p ((21 - 29) / 4 ≤ z ≤ (25 - 29) / 4) = p (-2 ≤ z ≤ - 1) = p (z ≤ - 1) - p (z ≤ - 2) = [1 - p (z ≤ 1) ] - [1 - p (z ≤ 2) ] = p (z ≤ 2) - p (z ≤ 1) = 0.97725 - 0.84134 = 0.13591 = 13.5%