# STATISTICS

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```					                                                   STATISTICS                                                            3.   The probability that the grocery store is closed at 6:00 pm is 0.42. The probabilities that the bank and
the shoe store are closed at 6:00 pm are 0.77 and 0.61 respectively. Find the probability that the bank
is closed and the grocery store and shoe store are open.
Use the following information to answer the next question.
A. 0.204                     B. 0.197               C. 0.174               D. 0.059
Henry played 24 golf games on the same course during each of two seasons. In the first season, his mean score was
78 with a standard deviation of 2.1. In the second season, his mean score was 74 with a standard deviation of 3.8.
Numerical Response
1.      What does the standard deviation of Henry’s scores over the two seasons indicate?                             3.   The probability that an egg is cracked is 0.13. The probability that exactly 2 out of a dozen eggs are
A.   His scores were more consistent in the first season.                                                          cracked, to the nearest hundredth, is _____.

B.   His scores were more consistent in the second season.
4.   Rina takes a multiple choice quiz with 7 questions. Each question has four choices. Unfortunately,
C.   His average score was better in the first season.
Rina left her glasses at home and could not read any of the questions so she had to guess on every
D.   His average score was better in the second season.                                                            question. The probability that Rina passed this quiz is

A. 0.013                     B. 0.071               C. 0.929               D. 0.987
2.      If a set of data has a standard deviation of 0, then
Numerical Response
A.   the mean of the data must be 0                    B. all of the data values are the same
4.   Stupar consistently makes 32% of the free throws that he takes when playing basketball. If he takes 9 shots
C.   the data values collected have a sum of 0         D. the z-score of the mean of the data is equal to 1        in a game then the probability that he will sink at most 2 shots, to the nearest hundredth, is __________.

Numerical Response
Use the following information to answer the next question.
5.   A survey determined that in a particular province, 7 out of 10 motorists have collision liability insurance
In a certain model of bicycle, the head post has 10 ball bearings that are each produced with a mass as close
coverage. In that province, if an accident involving 5 motorists occurs, then the probability that all 5
as possible to 10g. A quality check was performed on a particular bicycle, and the mass, in grams, of each
motorists have collision liability insurance coverage is, to the nearest hundredth, ________.
ball bearing was recorded as shown below.

9.6, 10.1, 9.8, 10.2, 10.0, 9.9, 9.5, 10.3, 10.1, 10.5
Numerical Response
Numerical Response                                                                                                     6.   On a chemistry test, the mean was 52 and the standard deviation was 7. If Paul’s z-score was -1.7 then his
actual mark on the exam, to the nearest tenth, was _________.
1.           The population standard deviation of these 10 ball bearings, correct to the nearest hundredth of a
gram, is ________________g.
5.   Alex wrote four diploma examinations. From his study of statistics, he knows that a comparison of
relative performance on the four different examinations is determined by the calculation of z-scores.
The exam results are shown in the table below
Use the following information to answer the next question                                       Subject                Provincial Mean             Standard Deviation               Alex’s Score
Chemistry 30                   62.1                         16.0                           65
A die was rolled 30 times and the following outcomes were recorded:                                                          English 30                    64.4                         12.8                           80
Math 30                      62.5                         17.4                           83
Number rolled              Frequency                                                 Physics 30                    66.6                         17.1                           77
1                         4
2                         7                                                     Alex performed best, relative to other students in the province in
3                         6
4                         3                                                     A. Chemistry 30             B. Physics 30          C. Math 30             D. English 30
5                         8
6                         2
Numerical Response
Numerical Response                                                                                                     7.   A test was given where the scores were normally distributed. A student received a mark of 68 which
2.     For the 30 times the die was rolled, the mean for the number rolled, to the nearest hundredth, is ______.           was 1.3 standard deviations above the mean. If the mean of the test was 63 then the standard deviation
of the test, to the nearest hundredth is ______.
Numerical Response
6.        If a set of data is normally distributed, what percent of the data lies between one standard deviation
below the mean and two standard deviations above the mean?                                                    11.         John scored in the top 5% of his class on the last math exam which was normally distributed. The
mean score of the exam was 68% and the standard deviation was 12%. The lowest mark that John
A. 48%                        B. 68%                 C. 82%                D. 95%                                         could have scored on this test, to the nearest tenth of a percent, is __________.

7.        The area of the shaded region, correct to the nearest hundredth, is
11. At the 1996 Summer Olympic Games, 16 teams represented their country in the Basketball
A. 0.39                                                                                                           Tournament. Each team has 20 players. The heights of these athletes were normally distributed with a
B. 0.55                                                                                                           mean of 191 cm and a standard deviation of 6.5 cm. The best estimate for the number of players in the
C. 0.68                                                                                                           tournament who were between 185 cm and 200 cm is
D. 1.63
A. 15                      B. 18                  C. 236                D. 293
z- scores       -0.20          1.83
12. Referring to the above question, if in the year 2004 every Basketball player at the Summer Games is 5
Numerical Response                                                                                                     cm taller, then
8.        The scores of an examination are normally
distributed. The diagram at the right indicates                                                                 A.   the mean will increase by 5 cm and the standard deviation will remain unchanged
the number of students who received scores                                                                      B.   the mean will remain unchanged and the standard deviation will increase by 5 cm
below the mean or above a particular z-score.                                                                   C.   the mean and the standard deviation will both increase by 5 cm
The z-score, to the nearest hundredth, is ______.                 1250                                          D.   the mean and the standard deviation will both remain unchanged
255
13. Police know that the speeds of cars in a 70 km/h zone are normally distributed with a mean of 73.5
km/h and a standard deviation of 3.5 km/h. A police officer needs to meet his monthly quota so he
decides to set up a radar speed trap in a 70 km/h zone. He records the speeds of 200 cars that pass by.
8.        Twenty percent of all aircraft have a top speed faster than 700 mph. Fifty percent of all aircraft have a         If the police officer allows cars to be 10% over the posted speed limit before stopping them, the
top speed faster than 400 mph. Find the percentage of aircraft with a top speed between 100 mph and               number of cars stopped for speeding would be
400 mph, if ten percent of aircraft are slower than 100 mph and the data is normally distributed.
A. 148                     B. 68                  C. 32                 D. 20
A. 90%                        B. 40%                 C. 20%                D. 10%
14. A manufacturer of C.D. players finds that the mean “life” of their product is 37 months. They
9.        The lengths of nails in two different boxes are normally distributed. The mean and standard deviation             guarantee the product for 24 months and find that only 3% are returned under this guarantee. If the
in the first box are 8.9 cm and 0.05 cm. The mean and standard deviation in the second box are 9.1 cm             data are normally distributed, then the standard deviation is approximately
and 0.03 cm. Which of the following statements below is false?
A. 2 months                 B. 7 months            C. 13 months          D. 24 months
A.      The lengths of nails in box two are more consistent.
B.      There is a greater probability of selecting a nail with a length of greater than 8.9 cm from box
two.                                                                                                  15. A normally distributed set of data has a mean of 81 and a standard deviation of 1. The value of z1 is
C.      There is an equal probability of randomly selecting a nail from box 1 that is between 8.80 cm and
8.95 cm as there is a nail from box 2 that is between 9.07 cm and 9.16 cm.                                   −0.88 . Find the value of z2 if it halves the area between z1 and 81.
D.      The area under the normal curve between 0 and 1 standard deviations for both boxes are unequal.
A. -1.01                   B. -0.44               C. -0.40              D. -0.24
10. A small airline has determined that the mass of luggage carried by passengers boarding an aircraft is
normally distributed with a mean of 15 kg and a standard deviation of 2.7 kg. The percentage of
passengers that will have luggage with a mass less than 12 kg is
A. 11.10%                     B. 13.33%              C. 36.65%             D. 38.90%

Numerical Response                                                                                                      Multiple Choice:                                         Numerical Response:
9.        The marks on a mathematics examination are normally distributed with a mean of 60% and a standard
deviation of 10%. Correct to the nearest hundredth, the probability (expressed as a decimal) that a student     1.A           2. B     3. C       4. B                 1. 0.29               2. 3.33               3. 0.28
scores between 54% and 72% on this examination is __________.                                                   5. D          6. C     7. B       8. B                 4. 0.41               5. 0.17               6. 40.1
9. D          10. B    11. C      12. A                7. 3.85               8. 1.27               9. 0.61
Numerical Response                                                                                                        13. C         14. B    15. C                           10. 25.3              11. 87.7
10. The lengths of fish in lake Mathy is normally distributed with a mean of 30 cm and a standard deviation of
3.7 cm. When you catch a fish in this lake, it must be above x cm or else you have to release it. If the
conservation officer wants approximately 10% of all fish caught to be released, then the value of x, to the
nearest tenth, is __________.

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