The local bakery bakes more than a thousand 1-pound loaves of bread daily, and t

Question

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 1.1 lb. and 3 oz., or 584 grams. Assume the standard deviation of the weights is 20 grams and a sample of 44 loaves is to be randomly selected. (e) What is the probability that the sample mean will have a value less than 582? (Give your answer correct to four decimal places.) (f) What is the probability that the sample mean will be within 6 grams of the mean? (Give your answer correct to four decimal places.)

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =20/(44)1/2 =3.015

e)therefore probability that the sample mean will have a value less than 582=P(X<582)=-P(Z<(582-584)/3.015)

=P(Z<-0.6633)=0.2536

f) probability that the sample mean will be within 6 grams of the mean =P(584-6<X<584+6)

=P(-6/3.015<Z<6/3.015)=P(-1.9900<Z<1.9900)=0.9767-0.0233 =0.9534

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