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# Probability and Statistics

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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) ______

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

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#### Solution Summary

Step by step solutions to all the problems is provided.

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1) When sending data over the internet there is a certain probability that a message will be corrupted. One way to improve the reliability of getting messages through is to use a Hamming Code. This involves sending extra data that can be used to check the main message. For example a 7 bit Hamming Code contains 4 bits of message data and 3 check bits. If only one of the bits is in error at the receiving end then mathematical techniques can be used to determine which one it is and apply a correction. Assume that you have a network connection for which the probability that an individual bit will get through without error is 0.66. What is the increase in the probability that a 4 bit message will get through if a 7 bit Hamming code is used instead of just sending the 4 bits? (i.e what is P(7 bits with 0 or 1 error) - P(4 bits with no error)?

2) Q Computers has invented quantum computers. Each computer contains an exotic sub-atomic particle. Unfortunately this particle decays in the same manner as all radioactive particles. Therefore an average quantum computer only lasts for 22 months. The University has purchased one of these computers and Professor Squiggle wants to use it for 7 months. When he tries to book it he finds that it is already booked out for the first 8 months. So he books it for the next 7 months. What is the probability that the computer will fail during the time that professor Squiggle is using it (not before and not after)?

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