Download Final exam Review (retesting for the last two tests – Statistics)

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Final exam Review (retesting for the last two tests – Statistics)
1.
The mean length of a normally distributed sample population of 3,700 boards is 26 inches and the standard
deviation is 11 inches. What percent of the population falls within 15 inches to 48 inches?
2.
A randomly-selected group of 8 people were formed. Each person was asked how many glasses of water
they drank each week. Their answers were: 7, 12, 18, 9, 10, 2, 5, 15. What is the standard deviation of this
sample?
3.
The scores on a university examination are normally distributed with a mean of 62 and a standard deviation
of 11. If the middle 68% of students will get a “C”, what is the lowest mark that a student can have and still
be awarded a C?
4.
Mr. Nelson’s math class had an average of 81 on the first test with a standard deviation of 3.6. Mr.
Matthews’s math class had an average of 82 on the first test with a standard deviation of 6.9. Which is
true in comparing the performance of the two classes?
(A) Mr. Nelson’s class did better than Mr. Matthew’s class.
(B) Mr. Matthew’s class did better than Mr. Nelson’s class.
(C) Mr. Nelson’s class had less spread in the scores than Mr. Matthew’s class.
(D) Mr. Matthew’s class had less spread in the scores than Mr. Nelson’s class.
5.
The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches
and standard deviation 2.5 inches. Half of all young men are shorter than
(A) 65.5 in
(B) 68 in
(C) 70.5 in
(D) can’t tell, the median height is not given
Use this data for questions 6 and 7.
The table below shows the heights in inches of samples of players taken from two basketball teams.
6.
What best describes the sample standard deviation for the Falcons?
(A) 2
(B) 3.74
(C) 4.18
(D) 70
7.
Which statement accurately compares the data?
(A) The mean height is the same for both teams.
(B) The mean height is greater for the Falcons than for the Eagles.
(C) The sample standard deviation is the same for both teams.
(D) The data set for the Falcons is more variable than the data set for the Eagles.
8. Avoiding an accident while driving can depend on reaction time. That time, measured from the moment the
driver notices the danger until he applies the brake, is thought to follow a normal model with a mean of 1.5
seconds and a standard deviation of 0.2 seconds.
a) Sketch a model for this situation.
b) What percent of drivers have a reaction time less than 1.3 seconds? ( 2 points)
c) What percent have reaction times between 1.7 and 1.9 seconds? ( 2 points)
9.
Ms. Mosher recorded the math test scores of six students as 78, 72, 80, 85, 93, and 80.
a) Determine the mean of the student scores, to the nearest tenth.
b) Determine the median of the student scores
c) Determine the standard deviation of the student scores, to the nearest tenth.
d) Describe the effect on the mean, median and standard deviation if Ms. Mosher adds 5 bonus points to
each of the six students’ scores.
10. What does the correlation value r for a regression line describe about the data?
(A)
(B)
(C)
(D)
It describes the accuracy of the data.
It describes the domain of the data.
It describes how closely the data fit the line.
It describes the range of the data.
11. In a normal distribution, the mean weight of 12-year old children is 85 pounds the standard
deviation is 4 pounds.
What weight is exactly 1 SD above the mean? Below the mean?
What weight is exactly 2 SD above the mean? Below the mean?
What percent of the children weigh less than 77 pounds?
What percent of the children weigh between 73 pounds and 89 pounds?
A weight of 80 pounds is above the ________ percentile but less than the ________ percentile.
Weights that would occur less than 5% of the time are __________.
12.
The Los Angeles Lakers won the 2002 NBA championship. This table gives the total points scored by each
player during that season.
Find the mean, median, mode, and standard deviation for this data set.
14.
13
15. For the average life expectancy in the United States to reach 100, 18% of people would have to live to age 120.
What standard deviation are we assuming for this statement to make sense?
A. 21.7
C. 25.2
B. 24.4
D. 35.0
16. 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. All units are in mg/100 mL, and the data are based on the National Health Survey.
If a man aged 18 to 24 is randomly selected, find the probability that his serum cholesterol level is between
100 and 200.
17. Which equation most closely fits the data in
the scatterplot?
A. 3 y  4 x  2
B. 3 y  6  4 x
3x
C. y  2 
4
D. 3 y  4 x  6
18. The cost of a ticket to Funland varies according to the season.
Which of the following conclusions about the number of tickets
purchased and the cost per ticket is BEST supported by the
scatterplot above?
A. The cost per ticket increases as the number of tickets
purchased increases.
B. The cost per ticket is unchanged as the number of tickets
purchased increases.
C. The cost per ticket decreases as the number of tickets
purchased increases.
D. There is no relationship between the cost per ticket and
the number of tickets purchased.
19.
20. On a scatter plot that compares tourism and the median price of homes for 10 years, you see that the number of
tourists visiting the city increased along with the median price of a home.
What can you infer from this data?
a. There is a positive correlation between tourism and home
prices.
b. There is no correlation between tourism and home prices
c. Increased tourism raised home prices
d. Higher home prices increased tourism
21. This graph plots the number of wins in the 2006 and 2007 seasons for a
sample of professional football teams. The linear regression model for
these data is y = 1.10x  2.29.
Based on this model, what is the predicted number of 2007 wins for a
team that won 5 games in 2006?
a. 3.2
b. 4.5
c. 5.5
d. 6.6
22.
When the data points are graphed, which has a negative correlation?
a. When the points form a vertical line
b. When the points fall from left to right
c. When the points form a horizontal line
d. When the points rise from left to right
23.
Where on a scatter plot with a positive correlation does an outlier appear?
a. Above the clustered majority of points
b. Below the clustered majority of points
c. Outside the clustered majority of points
d. In the clustered majority of points
24.
If the shoe size of all women between ages 18 to 24 are approximately normally distributed with a mean of
17.5 cm and a standard deviation of 2.8 cm, then ½ of all young women have a shoe size bigger than
______.
25.
If three consecutive integers, 13, 14, and 15 were given and you were told to find their mean, what happens
to the mean if 14 is added to the integers?
26.
Sketch a picture of skewed left, skewed right, and a normal distribution.
27.
When data is skewed right, which is bigger, the median or the mean?
28.
What numbers make up the five-number summary?
29.
What is x for the following ages: 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 16.
a. What is the variance of the sample ages?
b. What is the standard deviation of the sample ages?
c.
Create the normal distribution curve labeling mean, standard deviation, percentages, percentiles,
and describe the empirical rule.
30.
Find the mean AND sample standard deviation of the following: 72, 74, 76, 76, 75.
31.
Find the mean AND sample standard deviation of the following: 61, 62, 68, 69, 70.
32.
The amount of ketchup dispensed from a machine at CJ’s Hotdogs is normally distributed with a mean of
0.5 and a standard deviation of 0.3 ounces. If the machine is used 450 times, approximately how many
times will it be expected to dispense 1 or more ounces of ketchup?
33.
What does the correlation coefficient ( r) tell you?
34.
Give an example of positive correlation. (Not a number but a scenario that could be described as positive
correlation).
35.
Give an example of negative correlation. (Same as above)
36.
Give an example of an r value that is strongly, but negatively correlated.
37.
Give an example of an r value that is weakly, but positively correlated.
38.
What general form does an exponential regression equation look like?
39.
In an equation where the independent variable is time and the dependent variable is the number of laps
swam in a lap pool, what does slope represent in this situation? (In words).
40.
What would the y-intercept represent in this model between time and the number of laps?
41.
If the data is skewed left, which of the following is true about the mean and the median?
(A) The mean is greater than the median.
(B) The mean is less than the median.
(C) The mean equals the median.
(D) Not enough information is known.