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 1.2 lb. and 2 oz., or 601 grams. Assume the standard deviation of the weights is 25 grams and a sample of 46 loaves is to be randomly selected.

(a) This sample of 46 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 599 and 603? (Give your answer correct to four decimal places.)

  

(e) What is the probability that the sample mean will have a value less than 595? (Give your answer correct to four decimal places.)

  

(f) What is the probability that the sample mean will be within 2 grams of the mean? (Give your answer correct to four decimal places.)

Answer 1

Solution:- Given that mean = 601 grams, sd = 25, n = 46

(a) option B. approximately normal

(b) The mean of this sampling distribution = 601
μx = μ = 601

(c) THe standard errorof this sampling distribution
σx = σ/sqrt(n) = 21/sqrt(46) = 3.096 = 3.10 (rounded)

(d) P(599 < X < 603) = P((599-601)/3.10 < (X-μx)/σx < (603-601)/3.10 )
= P(-0.6452 < Z < 0.6452)
= 0.4844

(e) P(X < 595) = P(Z < (595-601)/3.10)
= P(Z < -1.9355)
= 1 − P(Z < 1.9355)
= 1 − 0.9738
= 0.0262

(f) for with in 2 grams

P(599 < X < 601) = P(-0.6452 < Z < 0.6452) = 0.4844