Round your answer to two decimal places Dartmouth Distribut

Round your answer to two decimal places.

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Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers.

It is known that 84% of all the orders it receives from its customers are delivered on time. Let (p-hat) be

the proportion of orders in a random sample of 100 that are delivered on time. Find the probability that

the value of (p-hat) will be between .81 and .87

Round your answer to four decimal places.

P(-15000<(xbar-mu)<15000)

= P(-15000/(80000/sqrt(70)) <(xbar-mu)/(s/vn) <15000/(80000/sqrt(70))

=P(-1.57<Z<1.57) = 0.88 (from standard normal table)

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P(0.81<phat<0.87)

= P((0.81-0.84)/sqrt(0.84*(1-0.84)/100) <(phat-p)/sqrt(p*(1-p)/n) <(0.87-0.84)/sqrt(0.84*(1-0.84)/100))

=P(-0.82<Z<0.82)

=0.5878 (from standard normal table)