Question

In Uganda only 9% of the population has access to electricity. Suppose we randomly sample 20 people in Uganda. Let X be the number of people in our sample who have access to electricity.

(a) What distribution will X have? (Hint: X only takes on the values 0, 1, ... 19, 20, so it can’t be a continuous distribution.)

(b) Find the mean and standard deviation for X . (

c) Find the probability that 10 people or less in the sample have access to electricity.

Answer 1

et x denotes the number of people in Uganda having access to electricity. X follows Binomial distribution with parameters and o.og respectively, u Binomial ( 20, 0.09) 20 k 0.09 of Binomial is given kan E The 2oXO:09 1.8 us 1.8 + Answer standard deviation of X calculated as a Sn nxp xul-b 1.2798 20x o.o 9x11-0.09) 52

c) Date P(x=x) = ncx p*(1-6 m-x For Binomial Distribution The probability that lo people less in the sample have access to electricity is calculated as = P ( x Llo) 20-X 20 10.09) (0-91) X 0 . 9 9 9 9 9 9 724801 1 Approximately I we can take. The probability that lo beople less im the sample have access to electricity is o 999999.