Question

hata persu is audited more than twice. 102, According to The world Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 people in Uganda. Let X the number of people who have access to electricity What is the probability distribution for X? b. a. Using the formulas, calculate the mean and standard deviation of x. c. Use your calculator to find the probability that 15 people in the sample have access to electricity d. Find the probability that at most ten people in the sample have access to electricity. e. Find the probability that more than 25 people in the sample have access to electricity 103. The literacy rate for a nation measures the proportion of people age 15 and over that can read and write. The literacy rate in Afghanistan is 281%. Suppose you choose 15 people in Afghanistan at random. Let X- the number of people who are literate. a. Sketch a graph of the probability distribution of X. b. Using the formulas, calculate the () mean and (i) standard deviation of X c. Find the probability that more than five people in the sample are literate. Is it is more likely that three people or four people are literate REFERENCES 4.2 Mean or Expected Value and Standard Deviation Class Catalogue att ible online at 30

Please

Answer 1

(10.2)

n = 150, p = 0.09, q = 1 - p = 0.91

P(x) = C(n, x) p^x q^(n - x)

(a) Probability distribution of x is a binomial distribution

(b) Mean = np = 150 * 0.09 = 13.5 and Standard deviation = √(npq) = √(150 * 0.09 * 0.91) = 3.505

(c) P(15) = C(150, 15) 0.09^15 0.91^(150 - 15) = 0.099

(d) P(x ≤ 10) = P(0) + P(1) + P(2) + ... + P(10)

= C(150, 0) 0.09^0 0.91^(150 - 0) + C(150, 1) 0.09^1 0.91^(150 - 1) + ... + C(150, 10) 0.09^10 0.91^(150 - 10)

= 0.2

(e) P(x > 25) = 1 - P(x ≤ 25)

= 1 - [C(150, 0) 0.09^0 0.91^(150 - 0) + C(150, 1) 0.09^1 0.91^(150 - 1) + ... + C(150, 25) 0.09^25 0.91^(150 - 25)]

= 0.00091