Question 1:

1.1. In the survey of 50 workers in BPC, the amount of wages per workers was recorded and the following data is obtained:

92          51          90          56          59          74          96          85          93          72

67          74          96          73          80          50          77          65          70          62

92          68          87          79          94          76          87          74          63          94

68          65          93          90          80          86          86          69          88          89

87          92          79          95          89          97          90          54          83          74

1.1.1 Compute group data mean   (15)

1.2. If it is estimated that 30% of all students who fall under the Business and Management Sciences

Faculty at Richfield have a valid driver’s license. What is the probability that in a sample of 10 students:

1.2.1.  Exactly 4 have a valid driver’s license?                                                                                         (5)

1.2.2.  At least 2 have a valid driver’s license?                                                                                         (5)

1.2.3. More than 9 have a valid driver’s license?                                                                                   (5)

QUESTION TWO                                                                                                                              (30 MARKS)

2.A batch of 5000 electric lamps has a mean life of 1000 hours and a standard deviation of 75 hours. Assuming a normal distribution:

2.1. How many lamps will fail before 900 hours?                                                                                 (10)

2.2. How many lamps will fail between 950 and 1000 hours?                                                            (10)

2.3. And given the same mean life, what would the standard deviation have to be to ensure that not more than 20% of lamps fail before 916 hours?                                                                        (10)

QUESTION THREE                                                                                                                        (30 MARKS)

3. Researchers at the European Centre for road Safety Testing are trying to find out how the age of cars affects their braking capability. They test a group of ten cars of differing ages and find out the minimum stopping distances that the cars can achieve. The results are set out in the table below:

car

Age (months)                       Minimum   stopping  at

40 km per hour

A                                              9                                              28.4

B                                              45                                            29.3

C                                              24                                            37.6

D                                             30                                            36.2

E                                              38                                            36.5

F                                              46                                            35.3

G                                             53                                            36.2

H                                             60                                            44.1

I                                               64                                            44.8

J                                               76                                            47.2

Using information provided above to answer the following questions:

3.1 Compute Pearson’s correlation coefficient.                                                                                          (15)

3.2 Compute Spearman’s correlation coefficient (rho)                                                                             (15)

Answers to Above Questions on Statistics

Answer 1: The group data mean is calculated as follows:

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