Last Exam Review Sheet:
1) For each of the following, sketch the areas under the standard normal curve over the indicated
intervals, and find the specified areas.
a) Between z = -2.12 and z = 1.55
b) Between z = 0 and z = -2.4
c) To the left of z = -1.23.
d) To the right of z = -1.15
e) P(0 < z < .45)
f) P(-1.34 < z < 2.79)
2) Convert each of the following to a z-score: (Use a mean of 114 and a standard deviation of
1.35.)
a) 116.75
b) 111.9
c) 114.76
d) 101.23
3) Convert each of the following to an x-score: (Use a mean of 85 and a standard deviation of
9.4.)
a) 1.23
b) -0.45
c) 2.22
d) -1.36
4) George is a senior citizen who takes medication to stabilize his (systolic) blood pressure. He
takes his blood pressure every day and from long experience, he knows the average pressure is
137 with standard deviation of 6. Assume the blood pressure follows a normal distribution. For
the past ten days his blood pressure has been recorded in the accompanying table, with x
representing the systolic blood pressure:
Day
x
1
128
2
133
3
130
4
134
5
139
6
140
7
139
8
142
9
158
10
161
a) Create a control chart for the systolic blood pressure readings and plot the data.
b) Do the data indicate the blood pressure distribution is “in control”? Explain you
answer!
5) At a large government office center in Chicago it has been found that the time employees
spend on the phone each day for business purposes has a normal distribution with a mean of 47
minutes and a standard deviation of 10 minutes.
a) If an employee is selected at random, what is the probability that he or she spends from
27 to 67 minutes on the phone each day?
b) If an employee is selected at random, what is the probability that he or she spends from
37 to 57 minutes on the phone each day?
c) What is the probability that he or she spends 47 minutes or fewer on the phone each
day?
6) At Burnt Mesa Pueblo, archaeological studies have used the method of tree ring dating in an
effort to determine when prehistoric people lived in the pueblo. Wood from several excavations
gave a mean year of 1,243 with a standard deviation of 36 years.
a) Estimate a range of years centered about the mean in which about 68% of the data will
be found.
b) Estimate a range of years centered about the mean in which about 95.4% of the data
will be found.
c) Estimate a range of years centered about the mean in which about 99.7% of the data
will be found.
7) Draw the normal curve when μ = 174 and σ = 17.
a) What is the percentage of area over the interval between 174 & 191?
b) What is the percentage of area over the interval between 191 & 208?
c) What is the percentage of area over the interval between 174 & 208?
d) What is the probability that the data will fall between 157 and 174?
e) What is the probability that the data will fall between 157 and 225?
8) Assume that z has a normal distribution, with the specified mean and standard deviation. Find
the indicated probabilities: (Include a sketch!)
P(142 < x < 149.5); μ = 145, σ = 2.2