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 1.5 lb. and 4 oz., or 794 grams. Assume the standard deviation of the weights is 21 grams and a sample of 35 loaves is to be randomly selected.

(a) This sample of 35 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution.

skewed right approximately normal     skewed left chi-square

(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.)
      grams

(c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.)


(d) What is the probability that this sample mean will be between 787 and 801? (Give your answer correct to four decimal places.)


(e) What is the probability that the sample mean will have a value less than 788? (Give your answer correct to four decimal places.)


(f) What is the probability that the sample mean will be within 5 grams of the mean? (Give your answer correct to four decimal places.)

Solution

(a)

Approximately Normal

(b)

Mean = 794 gms Answer

(c)

Standard Error = SD/sqrt(n) = 21/sqrt(35) = 3.55 Answer

(d)

z = (787-794)/3.55 = -1.9718 and

z = (801 - 794)/3.55 = 1.9718

P(787 < x < 801) = 0.9756 - 0.0244

= 0.9512 Answer

(e)

z = (788-794)/3.55 = -1.6901

P(x < 788 ) = 0.0455 Answer

As per the chegg Q&A guidelines I have answered first four subparts.