Download test 1 review problems

Mathematics 109 first test review problems
1. Identify the population & the sample in the following:
A study of 30, 000 insomniacs in the U.S. demonstrated that a poor diet contributed to the
lack of sleep.
2. A survey of 7000 people revealed that 350 people had a height over 75 inches.
(a) What is the frequency of heights over 75 inches?
(b) What is the relative frequency of heights over 75 inches?
3. Identify the numerical value as a parameter or as a statistic:
(a) 70% of Germans opposed lending more money to other countries, according to a phone
survey in which 2000 Germans were contacted.
(b) The mean first test score of this class will be 82%.
4. Weight data is collected from a group of one thousand adults.
The mean weight was found to be 120 pounds, and the standard deviation of the weights
was calculated to be 10 pounds.
The weight data has a symmetric bell-shaped distribution.
(a) Approximately what percent of the weights are between 110 and 130 pounds?
(b) Approximately what percent of the weights are in excess of 140 pounds?
(c) Approximately how many of the adults weigh less than 110 pounds?
5. Identify how you could collect data to
(a) determine the heights of adults in Seattle
(b) study the effect of drinking green tea on cancer rates.
6. A certain class determines the class average in the following way: 20% of the grade from
test 1, 20% from test 2, and 60% from the final exam. If the test 1, test 2, and final exam
scores were 70, 80, and 90, respectively, calculate the weighted average (or mean) of the
three scores.
page two
7. Identify the sampling technique:
(a) A study of political preferences is conducted at this college. Twelve classes are chosen
at random from the hundreds of classes, and each student in these twelve classes is
questioned.
(b) Border guards perform a thorough car search on every tenth car.
8. A sample of the three test scores 90, 85, and 30 is collected from a larger classroom.
Calculate from this small data sample
(a) the median
(b) the mean
(c) the range
(d) the variance
(e) the standard deviation
9. Draw a frequency histogram for the following class’ test score data:
test 1 score= x frequency
60 ≤ x < 70
2
70 ≤ x < 80
8
80 ≤ x < 90
7
90 ≤ x ≤ 100
3
10. For the following data set described by a dot plot
(a) calculate the range of the data
(b) what is the mode of the data?
(c) what is the median of the data?
(d) does the distribution skew to the left ? to the right?
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
100
110
120
page three
11. An ogive, or cumulative relative frequency graph, of a group of people’s ages is drawn
below. Use it to calculate
(a) the fraction of people whose age is between 10 and 20. ( 10 < age ≤ 20 )
(b) the fraction of people whose age is between 20 and 40. ( 20 < age ≤ 40 )
(40,1)
cumulative relative frequency
1
(30,0.80)
0.75
0.5
(20,0.45)
0.25
(10,0.15)
ages
-10
-5
0
5
10
15
20
25
30
35
40
45
50