A frequency distribution is shown below. Complete parts(a) through(e).

The number of overtime hours worked in one week per employee

Overtime hours

0

1

2

3

4

5

6

Employees

5

15

29

54

43

35

17

(a) Use the frequency distribution to construct a probability distribution.

x

0

1

2

3

4

5

6

(Round to the nearest thousandth asneeded.)

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Find themean, variance, and standard deviation of the binomial distribution with the given values of n and p.

n equals 80

n=80, p = 0.4

p=0.4

Themean,, is

. (Round to the nearest tenth asneeded.)

36% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is(a) exactlythree, (b) at leastfour, and(c) at most two. Ifconvenient, use technology to find the probabilities.

(a) P(3)=

36

36% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is(a) exactlythree, (b) at leastfour, and(c) at most two. Ifconvenient, use technology to find the probabilities.

(a) P(3)=

The times per week a student uses a lab computer are normallydistributed, with a mean of 6.1 hours and a standard deviation of 1.2 hours. A student is randomly selected. Find the following probabilities.

(a) Find the probability that the student uses a lab computer less than 5 hours per week.

(b) Find the probability that the student uses a lab computer between 7 and 8 hours per week.

(c) Find the probability that the student uses a lab computer more than 9 hours per week.

(a) The probability that a student uses a lab computer less than 5 hours per week is

Use the normal distribution of fish lengths for which the mean is 10 inches and the standard deviation is 4 inches. Assume the variable x is normally distributed.

(a)

What percent of the fish are longer than 14 inches?

(b) If 300 fish are randomlyselected, about how many would you expect to be shorter than 9 inches?

(a) Approximately % of fish are longer than 14 inches.

Use the normal distribution of fish lengths for which the mean is 10

10 inches and the standard deviation is 4 inches. Assume the variable x is normally distributed.

(a)

What percent of the fish are longer than 14inches?

(b)

If 300 fish are randomlyselected, about how many would you expect to be shorter than 9 inches?

(a) Approximately

% of fish are longer than 14 inches.

(Round to two decimal places asneeded.)

The annual per capita consumption of fresh apples(in pounds) in a nearby state can be approximated by a normaldistribution, with a mean of 17.1 pounds and a standard deviation of 4.3 pounds.

(a) What is the smallest annual per capita consumption of apples that can be in the top25% ofconsumptions?

(b) What is the largest annual per capita consumption of apples that can be in the bottom15% ofconsumptions?

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(a) Any per capita consumption of at least pounds is in the top25% of consumptions.

(Round to two decimal places asneeded.)