00:310 WhatsApp X Read Only - Save a copy to edit. Save a copy Instruction to Candidates Answer BOTH questions QUESTION ONE a) The data below represents the distribution profit levels (x) in millions of Kenya Shillings reported by a sample of 30 small and medium enterprises in Nairobi Profit levels (x) Number of firms (f) 2-4 2 4-6 16 6-8 10 8-10 Determine the mean and the standard deviation of the random variable (x) (10 Marks) b) Assuming the profit distribution in (b) above is governed by Normal Distribution, find and interpret the following probabilities i. P(3 X 7) (6 Marks) ii. P(8 x 12) (4 Marks) QUESTION TWO It has been widely being reported that 75% of all business startups in the hotel industry in Kenya claim that they generate a profit in their 2 years of operation. A sample of 6 new hotel business startups is randomly selected to enable an assessment of the probability that a given number of hotel startups generate a profit in their two years of operation. Let x be the number of hotel startups reporting making a profit in the 2 years operation. a) It is believed that the random variable x is governed by the binomial distribution. State why you think this is the most appropriate probability distribution for the random Variable (x)? (4Marks) = b) find the Probability Distribution of the random variable x and hence construct the corresponding histogram and interpret (6Marks) c) Using the result in (c) above, determine and interpret the following probabilities i. P(x 6) (3 Marks) ii. P(2 X 6) (4 Marks) d) Find the mean and the standard deviation of the random variable, x