130
Math 116 – 02: Test #2 (Chapters 6 – 8)
Spring 2012
Name:
Show work when appropriate. Correct answers with no support may not receive full points.
Use grammatically correct sentences when asked for explanations
1. Farmers measure daily production of milk in pounds. Guernsey cows average 39 pounds of
milk per day with a standard deviation of 8 pounds. For Jersey cows, the mean daily production
is 43 pounds with a standard deviation of 4 pounds. At a state fair, a champion Guernsey cow
and a champion Jersey cow each gave 54 pounds of milk. Which cow’s milk production was
more remarkable? Explain. (10 points)
2. Head circumferences for adult males are approximately normally distributed with a mean of
56cm and a standard deviation of 2cm. (5 points each)
(a) What is the z – score for a head circumference of 53.4cm?
(b) What is the head circumference corresponding to a z-score of 1.84?
(c) Explain, using the 68–95–99.7 rule why a head circumference of 62cm would be
considered unusual.
3. The typical amount of sleep per night for college students has a normally shaped distribution
with mean of 7 hours and standard deviation equal to 1.7 hours. Complete the following
statements. (6 points each)
(a) About 68% of typical college students sleep between
per night.
and
hours
(b) About 95% of typical college students sleep between
per night.
and
hours
(c) About 99.7% of typical college students sleep between
per night.
and
hours
4. Suppose that the distribution of speeds on a certain highway is normally shaped with a mean of
70mph and a standard deviation of 4 mph.
(a) Fill in the diagram representing the 68-95-99.7 rule in this scenario. You are to use this
diagram for the rest of this problem. (10 points)
(b) About what percent of speeds are between 62mph and 74mph?
(4 points)
(c) When a speed trap is set up on this highway, a driver will be pulled over if his/her speed
is in excess of 74mph. About what percent of drivers on this highway would be pulled
over when a speed trap is set up? (4 points)
(d) About what percent of speeds on this highway are between 58mph and 62mph?
(4 points)
(e) What speeds make up the highest 0.15% of all speeds on this highway?
(4 points)
5. Suppose that the amount spent on textbooks each term by students at a certain university is
normally distributed with a mean of $350 and a standard deviation of $100. Find each of the
following. NOTE: A 68-95-99.7 diagram will NOT be useful here.
(5 points each)
(a) What percent of students spend between $320 and $490 each term for textbooks at this
university?
(b) What percent of students at this university spend less than $170 each term for
textbooks?
(c) What percent of students at this university spend more than $700 each term for
textbooks?
(d) What amounts spent represent the highest 2% of all amounts spent by students at this
university for textbooks in a term?
6. The scatter plot below shows the relationship between a driver’s age and the average maximum
distance at which the driver could see a highway sign.
650
600
550
500
450
400
350
300
15
25
35
45
55
65
75
Age
(a) Write a sentence describing the apparent association between age and maximum
legibility distance. (5 points)
(b) Circle the most likely value of the correlation coefficient for this data.
r = 0.982
r = 0.745
r=0
r = -0.982
(4 points)
r = -0.745
7. For each of the following pairs of variables, is there likely to be positive association, negative
association, or no real association. Briefly explain your reasoning. (4 points each)
(a) height and grade point average of college students
(b) weight of a car and average number of miles it can go on a gallon of gas
8. The table below shows the latitude and average August temperature (in F) of 8 randomly
selected cities in the U.S. It is believed that there is a correlation between these two values.
Latitude
Temperature
26
83
31
82
33
85
35
81
39
76
41
76
45
71
47
68
(a) Find the linear regression equation and the
correlation coefficient to predict the average August
temperature in a U.S. city at latitude x. Round
numbers to 3 decimal places. (10 points)
(b) Comment on the strength of the linear relationship between these two variables. What
general trend do we see in the scatter plot, and is this supported by the value of the
correlation coefficient? (6 points)
(c) Use your model to predict the average August temperature in a U.S. city at a latitude of
42.8. (3 points)
(d) Explain why we should not use this model to estimate the average August temperature
of a U.S. city at a latitude of 60. (5 points)