You are concerned that your local coffee shop (of a chain) is spiking its coffee with extra caffeine. A spokesperson from the chain has stated the true mean amount of caffeine in a cup is 150 mg. Everyone agrees that the true population standard deviation is 5 mg. The manager of the local coffee shop cooperates with you. Both of you decide to randomly select 36 cups of coffee and compute the sample mean.

A. If the claim is correct, find

i. P(xbar > 152)

ii. P(xbar > 152.3)

B. The sample mean turns out to be 152.3 mg.  Do you think that the manufacturer’s claim is correct? Either your random sample was an aberration (included outliers) or the true mean amount of caffeine should be more than 150 mg. Explain why this makes sense.