Probability and Statistics Problems with Solutions

1) If a toy company is planning to introduce 3 new toys next Christmas. The toys sales can be a success or a failure, what is the probability that at least 2 of the toys are a success?

FFF FFS FSF FSS 4/8 = ½ = 0.5

S SFF SFS SSF SSS

For problems 2 and 3: a guitar manufacturer has an average daily production of 60 units, with a standard deviation of 7 units per day. If the guitar production distribution is mound shape:

2) What percentage of days in a month will have a daily production between 53 and 74 units?

53

3) What percentage of days in a month will have a daily production of more than 67 units?

x>67 = 16%

4) A combination lock system has three ten-digit (0 to 9) number wheels side by side. How many four-digit opening numbers are possible if a digit cannot be used more than once and the first digit cannot be number zero?

5x9x8 = 360

5) TOYA

6) A survey administered to technical staff at an electronic firm indicated that 23 individuals thought they were overpaid. 78 thought they were adequately paid, and 63 thought they were underpaid. If a person is selected at random, what is the probability that the person selected believes to be adequately paid.

23+78+63 = 164 P(AP) = 78/164 = 0.48

For problems 7, 8, 9, 10: a personnel manager constructed the table shown here to define nine combinations of talent-motivation levels from a testing survey of 1000 applicants for a company managerial position.

High medium low total

High

Medium

Low

Total

If he selects a person out of this group, what is the probability that:

7) The person selected is medium in talent?

= 530/1000 = 0.153

8) The person selected is high in talent given that the person is low in motivation?

P(A|B) = P(A and B) / P(B) >>> 110/1000 / 180/1000 = 110/180 = 0.61

9) The person selected is low in talent or medium in motivation?

P(A or B) = P(A) + P(B) - P(A and B)

= 120/1000 + 560/1000 - 50/1000 >>> 630/1000 = 0.63

10) The person selected is medium or low both in talent and motivation? #

P(Medium or low) = 320+50+50+20 / 1000 = 440/1000 = 0.44

11) TOYA

For problems 12, 13, 14: two fair dice are rolled. What is the probability that:

12) The sum of the numbers on the top face of both dice is exactly equal to 10?

55 64 46 >> 3/36 = 0.083

13) The sum of the numbers on the top face of both dice is greater than or equal to nine (9)?

45 65 36 64 P(x > 9) 10/36 = 0.27

54 56 63

55 66 46

14) At least one of the top face of the two dice shows number 3 #

6/36 + 5/36 = 11/36

15) An appliance store is going out of business and has 15 televisions left: 7 color consoles, 5 portable color sets and black and white sets. Assuming that each of the televisions has an equal chance of being selected, what is the probability that the first two televisions sold are portable color sets?

5/15 x 4/14 = 0.095

16) One hundred (100) members of a country club were surveyed to determine the pattern of use of its recreational swimming pool. The results were the following: 89 members use the golf course or the pool. 35 members use the golf course, and 75 members use the pool. How many members use both facilities, the golf course and the swimming pool.

89 golf or pool

33 golf P(A or B) = P(A) + P(B) - P(A and B)

75 pool 0.89 = 0.35 + 0.75 - P(A and B)

0.21 = P(A and B) >>> 21 members

17) TOYA

For problems 18, 19, 20: According to the U.S. Energy Association, the price of unleaded gasoline in a sample of 21 states in 2003 is given in the following table:

18) Calculate the mean or arithmetic average price of unleaded gasoline in the 21 states.

x = Σxi / n = 44.55 / 21 = 2.12

19) What is the median price of unleaded gasoline in the 21 states?

Median = ½ (21) = 10.5 ~ 11

Median = 2.05

20) What is the standard deviation for the price of unleaded gasoline in the 21 states?

98.76 - 1,984.70 / 21 / 20 >>> 98.76 - 94.51 / 20 = 4.25 / 20 = 17 / 80

s = 17 / 80 = 0.46