DHL Shipping claims that it ships 95% of its orders within three working days. You select a simple random sample of 100 orders and discover that only 91 of them shipped on time.

a) If DHL really does ship 95% on time, what is the probability that the company shipped 91 or fewer out of 100 orders were shipped on time?
b) A marketer from UPS jumps on the research stating, "They claim 95% on time, but by their own research they only ship 91% on time!" Provide a rebuttal to the UPS marketer in non-statistical terms.

Question

DHL Shipping claims that it ships 95% of its orders within three working days. You select a simple random sample of 100 orders and discover that only 91 of them shipped on time. 

a) If DHL really does ship 95% on time, what is the probability that the company shipped 91 or fewer out of 100 orders were shipped on time? 
b) A marketer from UPS jumps on the research stating, "They claim 95% on time, but by their own research they only ship 91% on time!" Provide a rebuttal to the UPS marketer in non-statistical terms.

anonymous · Answer

qa 
x is bin(100,0.95) 
P(x ≤91) = 6.31% <----- 

qb 
95% is a sort of average 
P(91 or more) is as high as 97.2%

anonymous · Answer

Thank you