The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches. a sample of 36 metal sheets is randomly selected from a batch. what is the probability that the average length of a sheet is between 29.82 and 30.27 inches long?

0.8490

Step-by-step explanation:

Given :  The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches.

i.e. and

Let x denotes the lengths of aluminum-coated steel sheets.

Required Formula :

For n= 36 , the probability that the average length of a sheet is between 29.82 and 30.27 inches long will be :-

∴ Required probability = 0.8490

7,24

step-by-step explanation:

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32