Question

Please read carefully. You must show all of your work for full credit. A correct answer with no work
shown is worth no points, but an incorrect or partial answer with some work shown may be worth
partial credit. Include explanations in each step.

Correct format for writing answers (using symbols and letters).

Question: What is the probability that fewer than 120 agreed?

Answer: P (x < 120)

I. An orange juice producer buys oranges from a large orange grove that has one variety of orange. The
amount of juice squeezed is approximately normally distributed, with a mean of 4.70 ounces, and a
standard deviation of 0.40 ounce.

a) What is the probability that a randomly selected orange will contain between 5.0 and 5.5
ounces of juice?

i. Probability statement:

ii. Calculations and draw:

b) 77 % or more of the oranges contain how many ounces of juice?

i. Calculations and draw:

c) Suppose that you select a sample of 25 oranges. What is the probability that the sample mean
amount of juice will be at least 4.6 ounces?

i. Calculate the mean and the standard deviation of the sampling distribution of x̅
and describe its shape.
μx̅=

σx̅=

Shape =
(Which rule apply: Sample comes from a population with a Normal distribution or because
The Central Limit Theorem)

ii. Probability statement:

iii. Calculations and draw:

2. The diameter of Ping-Pong balls manufactured at a large factory is approximately normally
distributed, with a mean of 1.30 inches and a standard deviation of 0.04 inch. If a random sample
of 16 Ping-Pong balls is selected from a population of 200 Ping-Pong balls, what is the probability
that the sample mean is between 1.31 and 1.33 inches?

i. Probability statement:

ii. Calculations and draw:

3. In a typical class, about 70% of students receive a C or better. Out of a random sample of 100
students, what is the probability that less than 60 receive a C or better?

i. Calculate the mean and the standard deviation of the sampling distribution of
pˆ and describe its shape.

 p
ˆ =

 p
ˆ =

Shape =(Which rule apply: Sample comes from a population with a Normal distribution or because
The Central Limit Theorem)

iii. Probability statement:

iv. Calculations and draw:

Answer 1