The local bakery bakes more than a thousand 1pound loaves of

The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 0.9 lb. and 4 oz., or 522 grams. Assume the standard deviation of the weights is 28 grams and a sample of 40 loaves is to be randomly selected.

A)What is the probability that the sample mean will be within 8 grams of the mean? (Give your answer correct to four decimal places.)

**I have asked this question 2 times and its wrong every time the last answer they gave me was .2282

Solution

Mean ( u ) =522
Standard Deviation ( sd )=28
Number ( n ) = 40
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 514) = (514-522)/28/ Sqrt ( 40 )
= -8/4.4272
= -1.807
= P ( Z <-1.807) From Standard Normal Table
= 0.03538
P(X < 530) = (530-522)/28/ Sqrt ( 40 )
= 8/4.4272 = 1.807
= P ( Z <1.807) From Standard Normal Table
= 0.96462
P(514 < X < 530) = 0.96462-0.03538 = 0.9292