Question

Suppose that the random variable X follows a normal distribution with mean 35 and variance 25.

a.) Calculate P(X > 37)

b.) Calculate P(32 < X < 38)

c.) Find the value of x so that P(X >x) is approximately 0.975

Answer 1

Solution :

Given that ,

mean = = 35

variance = 25

standard deviation = = 5

(a)

P(x > 37) = 1 - P(x < 37)

= 1 - P[(x - ) / < (37 - 35) / 5]

= 1 - P(z < 0.4)

= 0.3446

(b)

P(320 < x < 38) = P[(32 - 35)/ 5) < (x - ) /  < (38 - 35) /5 ) ]

= P(-0.6 < z < 0.6)

= P(z < 0.6) - P(z < -0.6)

= 0.415

(c)

P(Z < -1.96) = 0.025

z = -1.96

Using z-score formula,

x = z * +

x = -1.96 * 5 + 35 = 25.2

x = 25.2