Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 15.6; σ = 4.3

P(10 ≤ x ≤ 26) =

Answer 1

Solution:

Given:

μ = 15.6; σ = 4.3

P(10 ≤ x ≤ 26) = P(X<26) - P(X<10)

First find P(X<26)

Z = (X - µ)/σ

Z = (26 - 15.6)/4.3

Z = 2.418605

P(Z<2.418605) = P(X<26) = 0.99221

(by using z-table or excel)

Now find P(X<10)

Z = (X - µ)/σ

Z = (10 - 15.6)/4.3

Z = -1.30233

P(Z<-1.30233) = P(X<10) = 0.096403

(by using z-table)

P(10 ≤ x ≤ 26) = P(X<26) - P(X<10)

P(10 ≤ x ≤ 26) = 0.99221 - 0.096403

P(10 ≤ x ≤ 26) = 0.895807

P(10 ≤ x ≤ 26) = 0.8958