# Sampling and Sampling Distributions

In a sample of 25 observations from a normal distribution with mean 98.6 and standard deviation 17.2

Mary Bartel, an auditor for a large credit card company, knows that, on average, the monthly balance of any given customer is \$112, and the standard deviation is \$56.

In a sample of 16 observations from a normal distribution with a mean of 150 and a variance of 256, what is

In a sample of 19 observations from a normal distribution with mean 18 and standard deviation 4.8

In a normal distribution with mean 56 and standard deviation 21, how large a sample must be taken so that there will be at least a 90 percent chance that its mean is greater than 52?

In a normal distribution with mean 375 and standard deviation 48, how large a sample must be taken so that the probability will be at least 0.95 that the sample mean fails between 370 and 380?

An astronomer at the Mount Palomar Observatory notes that during the Gemind meteor shower, an average of 50 meteors appears each hour, with a variance of 9 meteors squared. The Geminid meteor shower will occur next week

The average cost of a studio condominium in the Cedar Lakes development is \$62,000 and the standard deviation is \$4,200.

1. What is the probability that a condominium in this development will cost at least \$65,000?
2. Is the probability that the average cost of a sample of two condominiums will be at least \$65,000 greater or less than the probability of one condominium’s costing that much? By how much?

Robertson Employment Service customarily gives standard intelligence and aptitude tests to all people who seek employment through the firm. The firm has collected data for several years and has found that the distribution of scores is not normal, but is skewed to the left with a mean of 86 and a standard devistion of 16. What i sthe probability that in a sample of 75 applicants who take the test, the mean score will be less than 84 or greater than 90?

An oil refinery has backup monitors to keep track of the refinery flows continuously and to prevent machine malfunctions from disrupting the standard deviation of 730 hours. In addition to the primary monitor the refinery has set up two standby units, which are duplicates of the primary one. In the case of malfunction of tone of the monitors, another will automatically take over in its place. The operating life of each monitor is independent of the others.