Statistics – Math 1530 Ch. 5,6 Practice Test Name:
Please only write your name on this sheet. All work and answers should be attached
on notebook paper.
1. If z follows the standard normal distribution (so
μ
=0, and
σ
=1), shade the appropriate area
and find the following:
a) The probability that z is between zero and 2.13
b) The probability that z is less than - 1.65
c) The probability that z is between - 1.09 and 1.32
d) The probability that z is greater than - 1.58
e) The probability that z is between - 2.03 and zero
f) The probability that z is greater than 15.65
g) Find the value of z that separates the top 40% of the distribution from the bottom 60%.
h) Find Q3, the 3rd quartile of the z distribution.
2. If x follows a normal distribution with a mean of 90 and a standard deviation of 12, find the
following:
a) The probability that x is between 90 and 98.
b) The probability that x is less than 95.
c) The probability that x is between 85 and 96.
d) The 25th percentile of the distribution.
3. The lifespans of a species of fruit fly are normally distributed, with a mean of 36 days and a
standard deviation of 4 days.
a) Find the probability that a random selected fruit fly lives more than 30 days.
b) Find the cutoff score that separates the 15% of the flies that live the shortest lives from the 85% of
the flies that live the longest lives.
4. The population mean annual salary for plumbers is $32,500. A random sample of 42 plumbers
is drawn from this population. What is the probability that the mean salary of the sample is less
than $30,000? Assume the standard deviation is $5600.
5. During a certain week the mean price of gasoline in Knoxville was $1.599 per gallon, with a
standard deviation of $0.095.
a) Find the probability that a randomly selected gas station charges more than $1.499 per gallon.
b) Find the probability that the average price of gas for 35 randomly selected gas stations is more
than $1.499 per gallon.
