# Probability and Statistics

Evaluate the permutation.

1) P( 9, 5) 1) _______

A) 9 B) 1 C) 504 D) 15,120

A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability.

2) All cherry 2) _______

A) .7272 B) .3636 C) .1091 D) .1212

In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev's theorem to tell the probability that a number lies in the following interval. Round your results to the nearest whole percent.

3) Between 26 and 74 3) _______

A) At least 90% B) At least 94%

C) At least 96% D) At least 93%

A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability.

4) 2 cherry, 1 lemon 4) _______

A) .1212 B) .7272 C) .1818 D) .3636

Find the standard deviation of the data summarized in the given frequency table.

5) A company had 80 employees whose salaries are summarized in the frequency table below. Find the standard deviation.

Salary Employees

5001- 10,000 20

10,001 - 15,000 15

15,001 - 20,000 10

20,001 - 25,000 13

25,001 - 30,000 22

5) _______

A) 8504.6 B) 8268.3 C) 7874.6 D) 8740.8

At one high school, students can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of .9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are:

6) Greater than 15.2 seconds 6) _______

A) 48% B) 68% C) 50% D) 34%

Evaluate the factorial.

7) 5! 7) _______

A) 24 B) 120 C) 240 D) 60

Find the requested probability.

8) A family has five children. The probability of having a girl is 1/2. What is the probability of having exactly 2 girls and 3 boys? 8) _______

A) .0625 B) .0312 C) .6252 D) .3125

Find the percent of the total area under a normal curve that is contained within the specified interval.

9) Between the mean and 3.01 standard deviations from the mean 9) _______

A) 49.86% B) 99.87% C) 49.87% D) 50.13%

Solve the problem.

10) Suppose there are 6 roads connecting town A to town B and 8 roads connecting town B to town C. In how many ways can a person travel from A to C via B? 10) ______

A) 14 ways B) 64 ways C) 48 ways D) 36 ways

11) If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated. 11) ______

A) 10,000 licenses B) 3024 licenses

C) 4960 licenses D) 5040 licenses

How many distinguishable permutations of letters are possible in the word?

12) MISSISSIPPI 12) ______

A) 831,600 B) 34,650 C) 69,300 D) 39,916,800

A die is rolled five times and the number of twos that come up is tallied. Find the probability of getting the indicated result.

13) Two comes up zero times. 13) ______

A) .0001 B) .424 C) .402 D) .161

A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the approximate number of bulbs that can be expected to last the specified period of time.

14) At least 500 hours 14) ______

A) 5000 B) 1000 C) 2500 D) 2400

A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result.

15) Exactly one four 15) ______

A) .402 B) .116 C) .502 D) .003

Find the standard deviation.

16) 14, 13, 20, 11, 18, 14, 19, 12, 6 16) ______

A) 4.4 B) 4.1 C) 4.7 D) 1.8

Find the percent of the total area under the standard normal curve between the given z-scores.

17) z = 0.0 and z = 3.01 17) ______

A) 0.4987 B) 0.1217 C) 0.9987 D) 0.5013

A die is rolled five times and the number of twos that come up is tallied. Find the probability of getting the indicated result.

18) Two comes up three times. 18) ______

A) .116 B) .003 C) .402 D) .032

Evaluate the combination.

19) 7

4

A) 210 B) 35 C) 12 D) 420 19) ______

Prepare a frequency distribution with a column for intervals and frequencies.

20) The following is the number of hours students worked per week at after-school jobs. Use five intervals, starting with 0 - 4.

20) ______

3 9 10 19 21 22 18 14 5 1 6 12 16 23 15 11 5 10 14 20

A)

Interval Frequency

0 - 4 2

5 - 9 3

10 - 14 7

15 - 19 4

20 - 24 4

B)

Interval Frequency

0 - 4 2

5 - 9 4

10 - 14 6

15 - 19 3

20 - 24 5

C)

Interval Frequency

0 - 4 2

5 - 9 4

10 - 14 5

15 - 19 5

20 - 24 4

D)

Interval Frequency

0 - 4 2

5 - 9 4

10 - 14 6

15 - 19 4

20 - 24 4

https://brainmass.com/statistics/probability-theory/probability-and-statistics-230136

#### Solution Summary

Step by step solutions to all the problems is provided.