Question

The lifetime of a certain battery follows a normal distribution with a mean 276 minutes and standard deviation 20 minutes. We took a random sample of 100 of these batteries. What is the probability that the sample mean of the lifetime will be less than 270 minutes?

A.0.9987

B.0.0013

C.0.4987

D.0.3821

Answer 1

Solution :

Given that,

mean = = 276

standard deviation = = 15

n = 100

=276

= / n = 20 100 = 2

P( < 270 )

P ( - /) < ( 270 - 276 / 2)

P ( z < - 6 / 2 )

P ( z < - 3)

= 0.0013

Probability =0.0013

Option B ) is correct.