Question

The literacy rate for a nation measures the proportion of people age 15 and over that can read and write. The literacy rate in Mali is 31%. Suppose you choose 25 people in Mali at random. a) Find the probability that in the sample of 25, exactly 10 of the people are literate. b) Find the probability that in the sample of 25, at most 10 are literate.

Answer 1

25 p=0.31 q=1-P=1-0.31 - 0.69 xn Binomial (no) q=0.69 w probability that in the sample of 25, exactly literate P(x = 10) q of people 20 x = R5 (0.3l) 10 (0.69) = (3268760) (0.00001) (0.00383 ) P(x = 10) 0.1025 Answer 10.10 0.1025 are (6) Probability that in the sample of 25 at most literate P(x = 10) =P(x=0) + P(x = 10 + P(x=2) + P(x=3) + P(x=4) + P(X=5+P (X=6) + P(x=7) + P(x=8) + P(x=9) + P(x = 10) 22 -25c60.31J°C0,6924+ 256, (0.31)'(0,69124 +255(0.31)2(069)"+ 256 (0.3)3 (0.693² +25c (0.3114 (0,69)² + 25 (0.31% (0.69) 20 -256, (0.31) (0.69) 19 + 250 254 (0.31)+ (0.69) +25€(0.2012 (0,69) 'c (0.31390.69) (0.31) (0,69) + 17 25 + g to + 25 to

=(1)(1)(0.00009) +(25) (0.31) (0.00014) t(300) (0.0961)(0.00020) +(2300)(0.02979) (0,00028) +(12650)(0.00929)00.00041) +53133)(0.00286) (096 060) +(177100)(0.00089) C0.00087)+(480700) (0.00028) (0.0013) +(1081575) (000009) (0.00182)+(2042975) (0.00003)(0.00264) +32 68760) (0.00001) (0.00383) 0.0000g +0.00105 +0.00567 to 61952 +0.04824 +0.og102 + o. 13631+ 0.16622 +0.16803 +0.14259 to.10250 p(x510) = 0.88124 Answer 10.881 88124