Question

Ask Your Teacher

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 2 lb. and 3 oz., or 992 grams. Assume the standard deviation of the weights is 30 grams and a sample of 35 loaves is to be randomly selected.

(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 988 and 996? (Give your answer correct to four decimal places.)


(e) What is the probability that the sample mean will have a value less than 986? (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 = = 992

standard deviation = = 30

n = 35

b) =   = 992

c) = / n = 30 / 35 = 5.07

d) P(988 < < 996)  

= P[(988 - 992) /5.07 < ( - ) / < (996 - 992) / 5.07)]

= P(-0.79 < Z < 0.79)

= P(Z < 0.79) - P(Z < -0.79)

Using z table,  

= 0.7852 - 0.2148

= 0.5704

e) P( < 986) = P(( - ) / < (986 - 992) /5.07 )

= P(z < -1.18)

Using z table

= 0.1190

f) 992 ± 2 = 990, 994

P(990 < < 994)  

= P[(990 - 992) /5.07 < ( - ) / < (994 - 992) / 5.07)]

= P(-0.39 < Z < 0.39)

= P(Z < 0.39) - P(Z < -0.39)

Using z table,  

= 0.6517 - 0.3483

= 0.3034