The randNorm function generates a random real number from a specified normal distribution. The syntax is ( mean, standard deviation [ , number of trials] ).

Problem 8: Suppose we are considering a normally distributed collection of IQ scores known to have a mean of 100 and a standard deviation of 15. Use randNorm to simulate the distribution of scores from a random sample of 100 people who have taken the test.

normalpdf( value [ , mean, standard deviation] )

normalcdf( lower bound, upper bound [ , mean, standard deviation] )

The normalpdf computes the probability density function for the normal distribution and the normalcdf computes the cumulative normal probability distribution between the lower bound and the upper bound. The default values for the mean and standard deviation in both are 0 and 1 respectively, thus creating the standard normal distribution. Both functions can be used to graph the distributions.

Problem 9: A company manufactures light bulbs that have a life expectancy that is normally distributed with a mean of 750 hours and a standard deviation of 40 hours. Find the probability that a bulb burns between 728 hours and 784 hours.

Problem 10: The heights of 6 year old girls are normally distributed with a mean of 46 inches and a standard deviation of 2.17 inches. Find the probability that a girl selected at random will have a height less than 44 inches.

Problem 11: In a letter to Ann Landers, a wife claimed to give birth to a baby 308 days after a visit from her husband who was in the Navy and stationed on board a ship. Pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Does the wife have a problem? (Triola, Elementary Statistics, Addison Wesley, 1992)

Problem 12: On a SAT exam administered by the CEEB, the mean math score was 475 with a standard deviation of 130. If a scholarship is available to students with scores above the 85th percentile, what is the score needed to be eligible for the scholarship?

Problem 13: The life of an electric drill when used commercially follows a normal distribution with a mean of 8 years with a standard deviation of 1.25 years. The manufacturer will replace free all drills that fail while under warranty. If the manufacturer is willing to replace only 5% of the drills that fail, how long a guarantee should be offered?