Suppose 27% of all small businesses are owned by a particular group of people. I

Question

Suppose 27% of all small businesses are owned by a particular group of people. In a random sample of 300 small businesses, let x be the number owned by that group. a. Find the mean of x. b. Find the standard deviation of x. c. Find the z-score for the value x = 99.5. d. Find the approximate probability that, in a sample of 300, x is 100 or more. a. The mean of x is about b. The standard deviation of x is about (Round to three decimal places as needed.) c. The z-score is about (Round to two decimal places as needed.) d. The probability is approximately (Round to four decimal places as needed.)

Explanation / Answer

Here p is 0.27 and n is 300

a) Mean is n*p =300*0.27=81

b) Standard deviation is sqrt(n*p*(1-p))=sqrt(300*0.27*(1-0.27))=7.69

c) z score is (99.5-81)/7.69=2.4

d) P(x>100) =P(z>(100-81)/7.69)=P(z>2.47) or 1-P(z<2.47)=1-0.932=0.068

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