Question

Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12 ounces and a standard deviation of 0.04 ounce. Use this information to answer the questions that follow.

Imagine that all possible samples of size 25 are taken from the population of this brewery’s 12-ounce bottles of beer.

Describe the sampling distribution of x ¯.

i. Center: μ x ¯=

ii. Spread: σ x ¯=  (round to 3 decimal places)

iii. What is the probability of randomly selecting a sample of twenty-five (25) 12-ounce bottles of beer with a mean of more than 12.02 ounces? (round to 3 decimal places)

iv. If you were to draw the distribution, you would shade to the  of the vertical line. Answer "left" or "right" without the quotations.

v. Interpret the probability from above “If 1000 samples of size 25 bottles were obtained from this population, we would expect about    sample(s) (round to the nearest whole number) to have a sample mean of more than  ounces.”

Answer 1

(iv) right

(v) 1000*0.006 = 6 (ans)