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COMP/ELEC/STAT 281
HISTORY OF NUMBERS AND GAMES OF CHANCE
FALL 2010
TR- 4:00-5:20PM
Tutorial Problems
Helpful source for normal distribution calculation: http://stattrek.com/Tables/Normal.aspx
1. The annual income of a random sample of five American households is $9, $27, $45, $72 and
$125 thousand dollars. Assume that household incomes are normally distributed with a standard
deviation of $60 thousand dollars.
 find the sample mean.
 construct a 90% confidence interval for the sample mean.
 construct a 95% confidence interval for the sample mean.
2. Waiting times (in hours) at a popular restaurant are believed to be approximately normally distributed
with a variance of 2.25 hr. during busy periods.
 A sample of 20 customers revealed a mean waiting time of 1.52 hours. Construct the 95%
confidence interval for the estimate of the population mean.
 Suppose that the mean of 1.52 hours had resulted from a sample of 32 customers. Find the
95% confidence interval.
 What effect does larger sample size have on the confidence interval?
3. A researcher is interested in whether or not high school students are passing a new statewide exit
exam. A random sample of 100 students has a mean of 76 and a standard deviation of 15. Calculate and
draw the 95% confidence interval around the mean. Can we be confident that the population mean is
above a passing grade of 70?
4. A drug company wants to know if its new drug lowers cholesterol below the target level of 120. A
random sample of 25 patients has a mean of 115 and a standard deviation of 20. Calculate and draw a
99% confidence interval around the mean. Can we be confident that the population mean is below 120?
Recalculate and redraw a 90% confidence interval around the mean. Can we be confident at this level?
5. Determine the 95% confidence interval for a sample with the following properties: N=36, X-bar=132,
variance (x-bar) =24. Draw the sampling distribution around a population mean of 120. Does the
population mean fall inside or outside the confidence interval?
6. The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the
heights of the population are random variables that follow a normal distribution with a variance of 0.16.

Determine the interval of 95% confidence for the average heights of the population.

With a confidence level of 90%, what would the minimum sample size need to be in order for the
true mean of the heights to be less than 2 cm from the sample mean?
7. The quantity of hemoglobin in the blood stream of a man follows a normal distribution with a standard
deviation of 2 g/dl. Calculate the confidence level for a sample of 12 men which indicates that the
population mean blood hemoglobin is between 13 and 15g/dl.
8. A college admissions officer for an M.B.A. program has determined that historically, applicants have
undergraduate grade point averages that are normally distributed with a population standard deviation of
0.45. From a random sample of 25 applications, the sample mean grade point average is 2.90.
 Find a 95% confidence interval for the population mean.
 Based on these sample results, a statistician computes a confidence interval for the population
mean extending from 2.81 to 2.99. Find the confidence level associated with this interval.
9. A business school placement officer wants to estimate the mean annual salary of the school’s former
students five years after graduation. Based on a random sample of 25 graduates it is found that the sample
mean salary is $42,740 and the sample standard deviation is $4,780.
 Assuming the population distribution is normal find a 90% confidence interval for the population
mean.