solve P(59<x<81)=P(-2<z<2.4)

Question

P(59<x<81)=P(-2<z<2.4)

Answer 1

Let mean = a and standard deviation be b.

P(59 < X < 81) = P(-2 < Z < 2.4)
P((59 - a) / b < Z < (81 - a) / b) = P(-2 < Z < 2.4)

Thus, we have:

(59 - a) / b = -2 --- (1)
(81 - a) / b = 2.4 --- (2)

From (2), we have:

81 - a = 2.4b
a = 81 - 2.4b --- (3)

Substituting (3) into (1), we will get:

(59 - 81 + 2.4b) / b =-2
-22 + 2.4b = -2b
-4.4b = -22
b = 5

Substituting b = 5 into (3), we will get:

a = 81 - 2.4(5)
a = 69

Hence, the mean is 69 and the standard deviation is 5.