Question

Cassandra's Cogs advertises on its website that 90% of customer orders are recived within three working days. They perfromed an adult from a random sample of 100 of the 2,500 orders that month and it shows 85 orders were recieved on time.

Part A: Can we use a normal approximation? Explain

Part B: If Cassandra's Cogs customers recieve 90% of their orders within three working days, where is the probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less?

Answer 1

Solution:

Cassandra's Cogs advertises on its website that 90% of customer orders are received within three working days. They performed an adult from a random sample of 100 of the 2,500 orders that month and it shows 85 orders were received on time.

Seams personal advertise on its website

P=90%=0.9.

Part A)

If the conditions that np>5 and n(1=p)>5 are met for binominal distribution.

Then a normal distribution can be used to approximate its probability distribution.

n*p=100*0.90

n*p=90>5

n(1-p)=100(1-0.90)=100(0.1)

n(1-p)=10>5

Both conditions are satisfied.

So,we can use normal approximation.

Part B)

If Cassandra's Cogs customers receive 90% of their orders within three working days, where is the probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit

=85/100=0.85

0.0485