Chapter 6 Review Sheet:
1) Sketch the normal curve and label all points of emphasis.
2) Sketch the standard normal curve and label all points of emphasis.
3) State four properties of the normal curve.
4) A toll free computer software support line for the spreadsheet Figure has established
target length of time for each customer help phone call. The calls are targeted to have a
mean duration of 7 minutes with standard deviation of 2 minutes. For one help
technician the most recent 10 calls had the following duration.
Call # 1
Length 8
2
15
3
10
4
4
5
6
6
4
7
8
8
12
9
10
10
12
a) Make a control chart showing the lengths of calls.
b) Is the chart “in-control”?
5) What percentage of the area under the normal curve lies
a) to the left of μ?
b) between μ- σ and μ + 2σ?
c) between μ - 2σ and μ?
6) Jan earned 86 on her political science midterm and an 89 on her chemistry midterm
exam. In the political science class the mean score was 75 with standard deviation of 4.
In the chemistry class the mean score was 80 with standard deviation of 9.
a) Convert each midterm score to a standard score.
b) Which score was higher with respect to the rest of the class?
7) For each of the following probabilities, shade the area under the standard normal curve
corresponding to the probability. Then find the requested probability.
a) P(z < 0)
b) P(-2.2 < z < 0)
c) P(-2.3 < z < 1.4)
d) P(z > 2.8)
e) P(0.8 < z < 2.3)
8) Let x represent the average miles per gallon of gasoline that owners get from the new
Nippon automobile. For this model the mean of the x distribution is advertised to be 44
mpg, with a standard deviation of 6 mpg. Convert each of the following x intervals to
standard z intervals and find the indicated probabilities.
a) x > 44
b) 40 < x < 50
c) 32 < x < 39