Question

Assume the random variable x is normally distributed with mean u=90 and standard deviation o=4. Find the indicated probability. ​P(77<x<86)

Answer 1

Solution:

We are given that random variable is normally distributed.

µ = 90

σ = 4

We have to find P(77<X<86)

P(77<X<86) = P(X<86) – P(X<77)

Find P(X<86)

Z = (X - µ)/σ

Z = (86 – 90)/4

Z = -4/4

Z = -1

P(Z<-1) = P(X<86) = 0.158655

(by using z-table)

Now, find P(X<77)

Z = (77 – 90) / 4

Z = -3.25

P(Z< -3.25) = P(X<77) = 0.000577

(by using z-table)

P(77<X<86) = P(X<86) – P(X<77)

P(77<X<86) = 0.158655 – 0.000577

P(77<X<86) = 0.158078

Required probability = 0.1581