Question

The amount of chocolates in a box from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 boxes is to be selected.

What is the probability that the sample mean will be greater than 100 grams?

Answer 1

Solution:

Given data:

normally distributed with μ = 110 grams

σ = 25 grams

n =  25 boxes

Now we have to find out the :

The probability that the sample mean will be greater than 100 grams:

sample mean will be greater than 100 grams X > 100

probability that the sample mean will be greater than 100 = P( X > 100 )

Now, P( X > 100 ) = $p( \frac{x-\mu }{\sigma } > \frac{x-\mu}{\sigma })$

=   $p( z > \frac{x-\mu}{\sigma })$

=  $p( z > \frac{100-110}{25 })$

= $p( z > \frac{-10}{25 })$

=   $p( z > -0.4)$

We know, p( x>a ) = 1-p(x<a)

  $p( z > -0.4)$  = $1-p( z < -0.4)$

From the z table we can get the value of - 0.4 is " 0.3446 "

= 1 - 0.3446

= 0.6554

$\therefore$ P( X > 100 ) =   0.6554

$\therefore$ Probability that the sample mean will be greater than 100 grams is " 0.6554 ".