Question

assume the random variable x is normally distributed with mean 80 and standard deviation 4. Find the indicated Probability P (70<×<76)

Answer 1

Solution:

We are given that the random variable X is normally distributed.

Mean = 80

SD = 4

We have to find P(70<X<76)

P(70<X<76) = P(X<76) – P(X<70)

First find P(X<76)

Z = (X – mean) / SD

Z = (76 – 80)/4 = -4/4 = -1

P(Z<-1) = 0.158655

(by using z-table or excel)

P(X<76) = 0.158655

Now find P(X<70)

Z = (70 – 80) / 4

Z = -2.5

P(Z<-2.5) = 0.00621

(by using z-table or excel)

P(X<70) = 0.00621

P(70<X<76) = P(X<76) – P(X<70)

P(70<X<76) = 0.158655 - 0.00621

P(70<X<76) = 0.152445

Required probability = 0.152445