Find the value of a

Question

let X be normally distributed with mean 75 in standard deviation five. Given that P(X<65)= P(X>a), find the value of a.

The answer choices are:

a) 60

b) -65

c) 85

d) 75

Answer 1

65 is two standard deviations to the left of the mean of 75. 85 is two standard deviations to the right of the mean of 75. Since the normal distribution is symmetric the area under the normal curve to the left of 65 and to the right of 85 will be equal.