Question

The number of loaves of bread sold per day by an organic bakery over the past five years can be treated as a random variable that is normally distributed. This distribution has a mean of 77.5 and a standard deviation of 14.4 loaves. Suppose a random sample of 36 days has been selected. Determine the probability that the average number of loaves sold in the sample of days exceeds 80 loaves. First find the standard error of the mean.

Now calculate the Z (Standard) Score. Round your answer to two decimal places

Now find the probability that the average number of loaves sold in the sample of days exceeds (is greater than) 80 loaves.

Answer 1

Solution :

Given that ,

mean = = 77.5

standard deviation = = 14.4

n = 36

= = 77.5 and

= / n = 14.4 / 36 = 2.4

z = ( - ) /

= ( 80 - 77.5 ) / 2.4

= 1.04

P( > 80) = 1 - P( < 80)

= 1 - P(( - ) / < (80 - 77.5) /2.4 )

= 1 - P(z < 1.04)

= 1 - 0.8508 Using standard normal table.

= 0.1492

Probability = 0.1492