Question

A large cooperation has quality control over its fertilizers. The fertilizes are composed of nitrogen. The fertilizer requires 3 mg of nitrogen. The distribution of the percentage of nitrogen is unknown with a mean of 2.5 mg and a standard deviation of 0.1. A specialist randomly checked 100 fertilizer samples.

What is the probability that the mean of the sample of 100 fertilizers less than 2 mg?

Answer 1

Solution:

Given that ,

= 2.5

= 0.1

A sample of size n = 100 is taken from this population.

Let be the mean of sample.

Since sample size is greater than 30 , the sampling distribution of the is approximately normal with

Mean() = =   2.5

SD() =    = 0.1/​100 = 0.01

Find P( < 2)

= P[( - )/ < (2 - 2.5)/0.01]

= P[Z < -50]

= 0.0000

P( < 2) = 0.0000