Question

1). Suppose we install a new billing system that we believe will have an average pay cycle of 19.5 days with a standard deviation of 4.2 days. If we draw a sample of 65 invoices from the population of paid invoices at our location, with a mean paid time of 18.107 days. If the population mean is actually 19.5 days what is the probability of observing a sample from that population with a mean of 18.07 days.

2). An automaker had drawn a sample of 50 cars with an average mpg of 31.56. He wants to know the probability that a sample with that mean mpg could have been drawn from a population with a mean mpg of 31 and a standard deviation of .8.

Answer 1

1)

Since normal distribution is continuous distribution so we cannot calculate exact probability observing a sample from that population with a mean of 18.07 days. The probability of getting sample mean 18.07 or more extreme need to be calculated.

2)