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Statistics and Probability Answers

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KPMG, an auditing firm has noticed that of the companies it audits, 85% show no inventory shortages, 10% show small inventory shortages and 5% show large inventory shortages. KK firm has devised a new accounting test for which it believes the following probabilities hold:

P (Company will pass test/no shortage) = 0.90
P (Company will pass test/small shortage) = 0.50
P (Company will pass test/large shortage) = 0.20

Required:
i) Determine the probability if a company being audited fails this test has large or small inventory shortage.

ii) If a company being audited passes this test, what is the probability of no inventory shortage?
Explain the assumptions of the linear regression model
Calculate the regression equation of X on Y (5 mks)
X 1 2 3 4 5
Y 2 5 3 8 7
A batch of 5000 electric lamps has a mean life of 1000 hours and a standard deviation of 75 hours.
Assume a normal distribution.
i) How many lamps will fail before 900 hours?
ii) How many lamps will fail between 950 and 1000 hours?
iii) What proportion of lamps will fail before 925 hours?
iv) Given the same mean life, what would the standard deviation have to be to ensure that no more than 20% of lamps fail before 916 hours
In Uthiru Girls an average 300 candidates do K.C.S.E every year. One out of the four streams claims that its candidates perform better in K.C.S.E than the rest of the candidates. If the proportion of the candidates who passed with at least ‘C’ out of the possible ‘A’ is 0.73 and the proportion of candidates from the stream consisting of 40 candidates is 0.78 (who passed with at least a ‘C’ grade). Is the stream’s claim true?
Suppose the annual savings (in millions of euros) of a specific household is a random variable, which follows the normal distribution with mean μ=5 and standard deviation σ=1. If we take a random sample of 16 households from the population, what is the probability the sampling mean to be:

more than 5.5 million euros?
between 4.9 and 5.1 million euros?
A passenger arrives at a bus stop at 10 am knowing that bus will arrive at random time between 10 am and 10:30 am. What is the probability that he will have to wait lower than 10 minutes?If the bus has not arrived until 10 : 15 am, what is the probability that he will have to wait another 10 minutes?
What does it take to win at sports? if you are talking about basketball, one sportwriter gave the answer. He listed the winning scores of the FIBA Africa Championships games over the last 35 years. The scores for those games are as follows: 132 118 124 109 104 101 125 83 99 131 98 125 97 106 112 92 120 103 111 117 135 143 112 112 116 106 117 119 110 105 128 112 126 105 102
a) Construct a stem and leaf plot of the scores (5)
b) Calculate the mean, median and mode of the data set. (6)
c) Calculate the standard deviation of the scores (5)
d) Determine the coefficient of variation (2)
e)The FIBA European Championships during the same period had an average winning score
of 102 with a standard deviation of 10. Which championship is more consistent and why? (4)
f) Group the winnings scores into classes 80 - 89 - 90 - 99 etc. until all the values have been accounted for.(3)
g) Construct a histogram of the data and comment on the shape of the distribution (5)
What does it take to win at sports? if you are talking about basketball, one sportwriter gave the answer. He listed the winning scores of the FIBA Africa Championships games over the last 35 years. The scores for those games are as follows: 132 118 124 109 104 101 125 83 99 131 98 125 97 106 112 92 103 111 117 135 143 112 112 116 106 119 110 105 128 112 126 105 102

a) Construct a stem and leaf plot of the scores (5)
b) Calculate the mean, median and mode of the data set (6)
c) Calculate the standers deviation of the scores (5)
d) Determine the coefficient of variation (2)
e) The FIBA European Championships during the same period had an average winning score
of 102 with a standard deviation of 10. Which championship is more consistent and why? (4)
f) Group the winnings scores into classes 80 - 89 - 90 - 99 etc, until all the values have been
accounted for. (3)
g) Construct a histogram of the data and comment on the shape of the distribution (5)
Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were as follows. 65 72 68 64 60 55 73 71 52 63 61 74
69 67 74 50 4 75 67 62 66 80 64 65

a) Calculate the quartiles of the data set (6)
b) Find the interquartile range (IQR) of the data (2)
c) Identify any outliers if present (5)
d) If there is/are outlier(s), what might be some explanation fo=r the outliers(s) (2)
e) Construct a box plot of the data set (4)
f) What information does the box plot deliver? (1)
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