SOLUTION: 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 3 oz., or 493 grams. Assume the st
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Question 1109857: 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 3 oz., or 493 grams. Assume the standard deviation of the weights is 22 grams and a sample of 30 loaves is to be randomly selected.
(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.)
(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 488 and 498? (Give your answer correct to four decimal places.)
(e) What is the probability that the sample mean will have a value less than 485? (Give your answer correct to four decimal places.)
(f) What is the probability that the sample mean will be within 3 grams of the mean? (Give your answer correct to four decimal places.)
You can put this solution on YOUR website! The mean of the sampling distribution is 493 gms. same as the point estimate
SE=sd/sqrt(n)=22/sqrt(30)=4.02 gms
z for 488=(488-493)/4.02=-1.24
z for 498 is +1.24
That probability is 0.7850
Less than 485 is z=(485-493)/4.02=-1.99
P(z<-1.99)=0.0233
within 3 gms of the mean is +/-z of 3/4.02 or +/-0.75
that probability is 0.5467 (or without rounding the z 0.5445; generally, we use z to two decimal places.)
