Question

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

μ = 26; σ = 4.4

P(x ≥ 30) =

Answer 1

Solution:-

We have

X has Normal distribution with

(Mean = , Standard deviation = )

Pdf of X is given by

Here, we have to find P(X>=30)=?

P(X>=30) = 1 - P(X<30)

By using Excel, the above probability can be calculated as

It gives value of probability

P(X>=30) = 0.18165107

Therefore,

P(X>=30) = 0.1817------(Rounded to 4 Decimal Point)

Note :

For normal distribution the probability

P(X<=x) = P(X<x) ......(both are equal)

This can be calculated by using Excel as