Question

Suppose X is a normal random variable with μ = 350 and σ = 40. Find the values of the following probabilities. (Round your answers to four decimal places.)

(a) P(X < 468)

(b) P(390 < X < 454)

(c) P(X > 390)

Answer 1

Given that X is a normal random variable with μ = 350 and σ = 40. hence the probability is calculated busing Z statistics.

a) P(X < 468) is calculated by finding the Z score at X = 468 as:

Thus P(X<468) =P(Z<2.95) is calculated using excel formula for norma distribution which is =NORM.S.DIST(2.95, TRUE), thus the probability computed is 0.9984.

b) P(390 < X < 454)

The Z scores are:

so, P(390 < X < 454) = P(1<Z<2.6) = P(X<2.6) -P(Z<1) is calculated using excel formula for normal distribution which is =NORM.S.DIST(2.6,TRUE)-NORM.S.DIST(1,TRUE), thus P(390 < X < 454) is computed from formula as 0.1540.

(c) P(X > 390), the Z score to calculated the probability is :

Thus P(X>390) =P(Z>1) is calculated using excel formula for normal distribution which is =1-NORM.S.DIST(1,TRUE), thus results in P(X>390) = 0.1587.