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 0.8 lb. and 2 oz., or 420 grams. Assume the st

Algebra ->  Probability-and-statistics -> 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 0.8 lb. and 2 oz., or 420 grams. Assume the st      Log On


   

Question 923678: 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 0.8 lb. and 2 oz., or 420 grams. Assume the standard deviation of the weights is 21 grams and a sample of 45 loaves is to be randomly selected.
(a) This sample of 45 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

Correct: Your answer is correct. .
.
(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 416 and 424? (Give your answer correct to four decimal places.)

(e) What is the probability that the sample mean will have a value less than 410? (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.)

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
mean = 420 grams. Assume the standard deviation of the weights is 21 grams
sample of 45 loaves is to be randomly selected.
(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.) 420gm
(c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.)
21%2Fsqrt%2845%29 = 3.13
(d) What is the probability that this sample mean will be between 416 and 424? (Give your answer correct to four decimal places.)
z = -4/3.13 = -.278 and z = 4/313 = .278
P(416 < x < 424)= normalcdf(-.278, .278) = .6068
(e) What is the probability that the sample mean will have a value less than 410? (Give your answer correct to four decimal places.)
P(x-bar < 410) =P(z < -10/3.13)= .0007
(f) What is the probability that the sample mean will be within 3 grams of the mean? (Give your answer correct to four decimal decimal places.)
P (417 x < 423) = normalcdf( -3/3.13, 3/3.13)= .6622