Answer to Question #203062 in Statistics and Probability for Erick

Question #203062

A survey claims that 73% of Fiji households have at least one credit card. Find the probability

that in a random sample of 550 Fiji households, 375 to 385 have at least one credit card.


1
Expert's answer
2021-06-07T01:44:22-0400

Let X=X= the number of households having at least one credit card: XBin(n,p)X\sim Bin(n, p)


P(X=x)=(nx)px(1p)nxP(X=x)=\dbinom{n}{x}p^x(1-p)^{n-x}

Given p=0.73,n=550p=0.73, n=550


P(X=375)=(550375)0.73375(10.73)550375P(X=375)=\dbinom{550}{375}0.73^{375}(1-0.73)^{550-375}

0.00159641506\approx 0.00159641506



P(X=376)=(550376)0.73376(10.73)550376P(X=376)=\dbinom{550}{376}0.73^{376}(1-0.73)^{550-376}

0.00200888518\approx 0.00200888518


P(X=377)=(550377)0.73377(10.73)550377P(X=377)=\dbinom{550}{377}0.73^{377}(1-0.73)^{550-377}

0.00250681398\approx 0.00250681398


P(X=378)=(550378)0.73378(10.73)550378P(X=378)=\dbinom{550}{378}0.73^{378}(1-0.73)^{550-378}

0.0031019551\approx0.0031019551


P(X=379)=(550379)0.73379(10.73)550379P(X=379)=\dbinom{550}{379}0.73^{379}(1-0.73)^{550-379}

0.00380613195\approx 0.00380613195


P(X=380)=(550380)0.73380(10.73)550380P(X=380)=\dbinom{550}{380}0.73^{380}(1-0.73)^{550-380}

0.00463079388\approx 0.00463079388


P(X=381)=(550381)0.73381(10.73)550381P(X=381)=\dbinom{550}{381}0.73^{381}(1-0.73)^{550-381}

0.00558648314\approx 0.00558648314


P(X=382)=(550382)0.73382(10.73)550382P(X=382)=\dbinom{550}{382}0.73^{382}(1-0.73)^{550-382}

0.00668222246\approx 0.00668222246


P(X=383)=(550383)0.73383(10.73)550383P(X=383)=\dbinom{550}{383}0.73^{383}(1-0.73)^{550-383}

0.00792484056\approx 0.00792484056


P(X=384)=(550384)0.73384(10.73)550384P(X=384)=\dbinom{550}{384}0.73^{384}(1-0.73)^{550-384}

0.00931826112\approx 0.00931826112


P(X=385)=(550385)0.73385(10.73)550385P(X=385)=\dbinom{550}{385}0.73^{385}(1-0.73)^{550-385}

0.01086278867\approx 0.01086278867


P(375X385)0.0580255911P(375\leq X\leq 385)\approx0.0580255911


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