The manager of a Papa John’s knows that for any order, there is a 95% chance tha

Question

The manager of a Papa John’s knows that for any order, there is a 95% chance that it is prepared without mistakes and delivered in under 45 minutes. (Let P = # pizzas delivered on-$me and correct.) On an average night, he delivers 120 orders. a) What’s the expected number of pizzas that will be delivered correctly under 45 min each night? b) Out of 120 orders, what are the possible number of pizzas that could be delivered correctly and on $me (the possible values of P)? c) Without doing any calcula$ons, what 3-4 values of P are most likely? d) (With calcula$ons…) What values of P are expected to happen >10% of the $me? e) What range of values for P are expected to happen more than 1% of the $me?

Explanation / Answer

a)E(x) = n*p = 120*0.95=114

b) The possible values of p are all values from 0 to 120

c) 3-4 values that are most likely are the ones around the mean , namely 113,114,115 etc

4) sigma = sqrt( npq) = sqrt( 120*0.95*0.05) = 2.38. Required value of z can be found from normal distribution tables.

z = -1.281551

x-114/ (2.38/sqrt(120) = -1.281551

or x =114- 1.28851*2.38/sqrt(120) = 113.72

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