Question

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%

Answer 1

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%