Question

Average area covered by a can of 1-gallon paint is 513.3 sq ft with a variance of 992.25 sq ft. Ascertain the probability that the mean area covered by a sample of 40 of these 1-gallon cans will be between 510 to 520 sq ft?

Answer 1

Given:- average area covered by a can of 1 gallon paint = =513.3 sq ft

And variance = =992.25

n =40

We want mean area covered between 510 to 520 sq ft .

Answer:-   = 513.3 sq ft

= 992.25

therefore ,   = 31.5

Since there is no reason to suspect that the single can paint coverage distribution is highly skewed, a 40 can sample will certainly allow the central limit theorem to kick in, so that the sample distribution of the mean will be normal.

So now calculate z-score value for 510 and 520 ft^2 value,

Hence , the probathat the mean area covered by a sample of 40 of these 1 gallon cans will be between 510 to 520 sq ft is 0.66 .