Name: ______
Test #3a – Spring 1998
Math 5
Instructions: Please show all work necessary to complete each problem on this paper. If additional space is needed please use the back of the test paper and label your problem clearly. Part of the assigned points will be for showing your work using correct notation, so correct answers will not give you full credit, or even partial credit – there must be work shown that supports each answer. Please box your final answer. Good luck.
1. A medical doctor randomly selects nine healthy patients and takes their temperatures.
Their temperatures are as follows:
98.6, 98.6, 98.0, 98.0, 99.0, 98.4, 98.4, 98.4, 98.6
a) For the sample find the sample mean. Show how you arrive at your answer.
b) Find the sample standard deviation. Show how you arrive at your answer.(You
may use your calculator to find x and x2)
c) Find a 95% confidence interval for the true population body temperature, given the
sample above, and assuming that the population is approximately normal with a
known standard deviation = 0.76.
d) Find a 95% confidence interval for the true population body temperature, given the
sample above if we only know that the sample is approximately normal.
2. Consider the picture of the uniform distribution given below.
a) Find the height of the density curve. Show your work in finding the height
and explain how you know what to do in order to find the height.
b) Find the probability of getting an x larger than two.
c) Find the probability of getting an x between -1 and 1.
3. A survey of 865 voters reveals that 408 favor approval of an issure before the
legislature.
a) Find the proportion of voters in the sample that favor the issue.
b) Construct a 90% confidence interval for the true proportion of all voters in the state
who favor approval.
4. For the next 100 births in the U.S. give the following:
a) What is the probability that a girl is born?
b) Find the average number of girls born ().
c) Find the standard deviation the number of girls born ().
d) Estimate the probability that there are at least 55 girls.
5. A teacher gives a test and gets normally distributed results with a mean = 50 and a
standard deviation = 10. Find the test score representing the following:
a) Q1
b) P90
c) The score separating the top 68% from the bottom 32%
6. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
Mensa is an organization of people with high IQ's , and eligibility requires an IQ above
131.5.
a) What percentage of the population is eligible for Mensa membership?
b) In a typical region of 30,000 people, how many would be eligible (to the nearest
whole person)?
7. The serum cholesterol levels in men aged 18 to 24 are normally distributed with a mean
of 178.1 and a standard deviation of 40.7.
a) Find the probability that a randomly selected man will have a cholesterol level less
than 200.
b) If a sample of 20 men is taken what is the probability that the average cholesterol
level will be greater than 200?
8. For a standard normal variable, find the probability that:
a) The random variable lies between -2 and -1
b) The random variable lies above -2
c) The random variable lies between -1 and 2.