Question

A pretzel company calculated that there is a mean of 75.4 broken pretzels in each production run with a standard deviation of 5.2. If the distribution is approximately normal, find the probability that there will be fewer than 66 broken pretzels in a run.

Answer 1

P [ Z < 66 ] = 35,15 %

Explanation:

Normal Distribution

Population mean μ₀ = 75,4

Standard deviation σ = 5,2

Then:

P [ Z < 66 ] = ( 66 - 75,4 ) / 5,2

P [ Z < 66 ] = - 9,4 / 5,2

P [ Z < 66 ] = - 1,81

In z-table we look for the reciprocate area for that z score and find

P [ Z < 66 ] = 0,3515

P [ Z < 66 ] = 35,15 %