Posted by Betty on .
The amount of time it takes to take your order at the local Whaters restaurant has a population mean m of 3.1 minutes and a standard deviation s of 0.40 minutes. If you select a random sample of 16 customers:
Q-3a: What is the probability that the mean time spent per customer is at least 3 minutes?
It is not mentioned that the distribution is normal. We will assume that it is, either by assumption, or by an approximation using the central limit theorem (which preferably applies to samples of 30+).
With the assumption, we can see that the variance is σ²/n=0.4²/16=0.01, hence σ=0.1.
Look up the Normal distribution table for 1-tail probability of 1σ which gives the probability of 1-0.8413=0.1587 for less than μ-1σ=3.1-0.1=3.0 minutes.
Can you take it from here?