Question

On a test that has a normal distribution, a score of 32 falls three standard

deviations below the mean, and a score of 82 falls two standard deviations
above the mean. Determine the mean of this test.

Answer 1

Mean = 62

Explanation:

X = mean ± sd

82 = mean + 2(s.d) - - (1)

32 = mean - 3sd ___(2)

82 = mean + 2sd

82 - 32= 2sd + 3sd

50 = 5sd

sd = 50/5

sd = 10

From (2):

32 = mean - 3sd

32 = mean - 3(10)

32 = mean - 30

32 + 30 = mean

62 = mean