The owner of the West End Kwick Fill Gas Station wishes to determine the proportion of customers who pay at the pump using a credit card or debit card. He surveys 100 customers and finds that 80 paid at the pump. a. Estimate the value of the population proportion. b. Develop a 95% confidence interval for the population proportion. c. Interpret your findings

n = 100 customers

X = 80 who paid at the pump

A) the sample proportion = p = X / n = 80 / 100 = 0.8

we can definitely state that 80% of the customers paid at the pump.

B) if we want to determine the 95% confidence interval:

z (95%) = 1.96

confidence interval = p +/- z x √{[p(1 - p)] / n}

0.80 +/- 1.96 x √{[0.8(1 - 0.8)] / 100}

0.80 +/- 1.96 x √{(0.8 x 0.2) / 100}

0.80 +/- 1.96 x √{(0.8 x 0.2) / 100}

0.80 +/- 1.96 x 0.4

0.80 +/- 0.0784

confidence interval = (0.7216 ; 0.8784)

C) We can estimate with a 95% confidence that between 72.16% and 87.84% of the customers pay at the pump.

(a) when insurance is obtained through a reciprocal insurer, the insureds are sharing the risk of loss with other subscribers of that reciprocal.

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