The local bakery bakes more than a thousand 1-pound loaves of bread daily, and t
ID: 3056302 • Letter: 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 1.8 lb. and 2 oz., or 873 grams. Assume the standard deviation of the weights is 30 grams and a sample of 30 loaves is to be randomly selected.
(a) This sample of 30 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 866 and 880? (Give your answer correct to four decimal places.)
(e) What is the probability that the sample mean will have a value less than 871? (Give your answer correct to four decimal places.)
(f) What is the probability that the sample mean will be within 4 grams of the mean? (Give your answer correct to four decimal places.)
Explanation / Answer
=873
=30
n=30
a)
The shape of this sampling distribution is approximately normal
b) sample mean =mean =873
c) standard error =/n =30/30 =5.48
d) P(866<x<880)
For x=866
z=(x-)/(/n)
=(866-873)/5.477
=-1.28
For x=880
z=(x-)/(/n)
=(880-873)/5.477
=1.28
P(866<x<880) =P(-1.28<z<1.28)
=P(z<1.28) -P(z<-1.28)
=0.8997 - 0.1003
=0.7994
e)
For x=871
z=(x-)/(/n)
=(871-873)/5.477
=-0.365
P(x<871) =P(z<-0.37)
=0.3557
f) within 4 grams means that x=873-4 to 873+4
or 869 to 877
For x=869
z=(x-)/(/n)
=(869-873)/5.477
=-0.73
For x=877
z=(x-)/(/n)
=(877-873)/5.477
=0.73
P(869<z<877) =P(-0.73<z<0.73)
=P(z<0.73) -P(z<-0.73)
=0.7673 -0.2327
=0.5346
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