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 4 oz., or 612 grams. Assume the standard deviation of the weights is 26 grams and a sample of 50 loaves is to be randomly selected.

(a) This sample of 50 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 604 and 620? (Give your answer correct to four decimal places.)

(e) What is the probability that the sample mean will have a value less than 606? (Give your answer correct to four decimal places.)

(f) What is the probability that the sample mean will be within 7 grams of the mean? (Give your answer correct to four decimal places.)

Answer 1

a)

approximately normal

b)

mean of this sampling distribution =612 gm

c)

standard error of this sampling distribution =std deviation/sqrT(50)=26/sqrt(50)=3.68

d)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	612
std deviation   =σ=	3.680

probability that this sample mean will be between 604 and 620:

probability =

P(604<X<620)

=

P(-2.17<Z<2.17)=

0.9850-0.0150=

0.9700

( please try 0.9704,0.9702 if this comes wrong)

e)

probability =

P(X<606)

=

P(Z<-1.63)=

0.0516

f)

probability =

P(605<X<619)

=

P(-1.9<Z<1.9)=

0.9713-0.0287=

0.9426