Question

Cassandra's Cogs states in its advertisement that 90% of its orders are ready to ship within three working days. A simple random sample of 100 of the 2,500 orders received during the past month are pulled for an audit. The audit shows that 84 of these orders were shipped on time.

**Part A:** If Cassandra's Cogs really ships 90% of
its orders within three working days, what is the probability that
the proportion in the simple random sample of 100 orders is as
small as the proportion in the auditors' sample or smaller?

**Part B:** A customer says, "Cassandra's Cogs
claims 90% of its orders are shipped on time, but its sample
proportion is less than that." Explain why the probability
calculation shows the result of the sample agrees with the 90%
claim.

Answer #1

a)

population proportion ,p=0.9

n=100

std error , SE = √( p(1-p)/n ) = 0.0300

sample proportion , p̂ =84/100 = 0.84

Z=( p̂ - p )/SE= (0.840-0.9) / 0.030=-2.000

P ( p̂ < 0.840) =P(Z<( p̂ - p )/SE) =

=P(Z < -2.000) **= 0.0228 (answer)**

b)

an SRS of 100 orders will have 84 or less on time about 2.28% of time

because of variation from sample to sample , we'll get values below 84 even if it is true

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