Can someone check my answers ?
Your mail-order company advertises that it ships 95% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit. The audit reveals that only 91 of these orders were shipped on time.

A) What is the sample proportion of orders shipped on time?

B) If the company really ships 95% of its orders on time, what is the probability that the proportion in an SRS of 100 orders is as small as the proportion in your sample or smaller? (Use a normal approximation, but be sure to justify the standard devi

Question

Can someone check my answers ? 
Your mail-order company advertises that it ships 95% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit. The audit reveals that only 91 of these orders were shipped on time. 

A) What is the sample proportion of orders shipped on time? 

B) If the company really ships 95% of its orders on time, what is the probability that the proportion in an SRS of 100 orders is as small as the proportion in your sample or smaller? (Use a normal approximation, but be sure to justify the standard devi

anonymous · Answer

A) 0.91 


B) P(≤91.5)=P(z≤91.5-95/2.179)=p(z≤-1.6)=.054
  
C) If it was less than 5% we could not support that claim. That's not likely to happen in a population with 95 % true shipping performance. In this case 5.4% so we can probably support the claim.