The probability based on normal distribution and standard deviation

Question

The amount of money spent per hour follows a normal distribution with a mean of $18 and standard deviation of $4. What is the probability that the average spending of 5 random customers will be more than $20 per hour ?

Answer 1

We are trying to find the probability that x=average spending of customer is greater than 20$.

Compute z-score: (sample mean - population mean)/(population standard deviation/square root of sample size), where sample mean = 20, population mean = 18, population standard deviation = 4 and sample size = 5.

Then use the normal probability table to compute P(z > computed z-score).

If have TI-83/84 calculator, you would enter normcdf(20,9999,18,4) to compute the probability directly.