MATH 1410 / MATH1410 STATISTICS
UNIT 2 – MILESTONE 2
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The manager went over the sales of mobile phones
... [Show More] at the store and found that the mean sale was 45, with a standard deviation of 4. On a particular day, 52 mobile phones were sold.
What is the z-score of the sale of mobile phones on that day?
-28
28
1.75
-1.75
RATIONALE
Recall that the z-score can be calculated with the following formula:
The given value is 52 phones, the mean is 45 phones, and the standard deviation is 4 phones. Plug these values in to get the following z-score:
This also tells us that 52 is 1.75 z-scores or standard deviations above the mean.
CONCEPT
Standard Scores and Z-Scores I need help with this question 2
In a poll of 300 preschoolers, 125 said they preferred chocolate ice cream, 71 said they preferred vanilla, 100 said they preferred cookies & cream, and 4 said they had never eaten ice cream.
If a pie chart were to be made showing the preference for each flavor, the central angle for the chocolate ice cream sector would be .
41°
5°
150°
124°
RATIONALE
Recall that to get the angle for something in a pie chart we use the following formula:
open parentheses fraction numerator v a l u e over denominator t o t a l space v a l u e end fraction close parentheses times 360 degree
So in this case, the central angle for the chocolate ice cream sector would be:
CONCEPT
Bar Graphs and Pie Charts
I need help with this question 3
The first quartile (Q1) value from the above box plot is .
47
40
65
54
RATIONALE
Note the value for Q1 is the left edge of the box, which is 47.
CONCEPT
Five Number Summary and Boxplots I need help with this question
4
Select the statement that accurately describes unimodal distribution.
A distribution in which two distinct values are more frequent than the other values.
A distribution in which the values are distributed uniformly.
A distribution in which one value is more frequent than other values.
A distribution in which numerous values are more frequent than other values.
RATIONALE
Recall the mode is the most frequently occurring value. If a distribution is unimodal, it simply means there is one value that occurs most frequently.
CONCEPT
Shapes of Distribution
I need help with this question 5
Choose the statement that correctly describes a normal distribution.
Approximately 68% of the values are greater than the mean value.
The approximate percent of values lying within three standard deviations of the mean is 49.85%.
Approximately 68% of the values lie within one standard deviation of the mean.
The approximate percent of values lying within two standard deviations of the mean is 47.5%.
RATIONALE
The normal distribution follows the empirical rule. This tells us that within one standard deviation of the mean, we should find roughly 68% of the data.
CONCEPT
Normal Distribution
I need help with this question 6
Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly.
The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is
.
68%
28%
34%
14%
RATIONALE
To get the relative frequency of 20 or lower, we need to find the cumulative number of 20 or less. We simply add up any bin that has the number 20 or less, such as the bin that shows scores of 1-5, 6-10, 11-15, and 16-20.
This would be:
To get relative frequency, we will take this cumulative number and divide it by the total number of students.
CONCEPT
Cumulative Frequency
I need help with this question 7
Dave drives to work. While driving the car over nine days, he observes his daily average speed and lists it in the table below.
Day Average Speed
(MPH)
1 45
2 62
3 44
4 70
5 59
6 66
7 54
8 63
9 67
The median speed at which Dave drove to work was .
62 miles per hour
58.89 miles per hour
59 miles per hour
63 miles per hour
RATIONALE
To get the median we first order the data and take the middle value. The ordered values are:
Since there are an odd number (n=9) of values we simply take the middle, which is 62 mph.
CONCEPT
Mean, Median, and Mode
I need help with this question 8
Which of the following statements is true?
For a large enough sample size, the Central Limit Theorem states that the sample medians of repeated samples of a population are normally distributed.
For the Central Limit Theorem to be true, you must have a large sample, the underlying population must be normally distributed, and the standard deviation should not be finite.
Even with a very large sample size, the Central Limit Theorem states that the sample means of repeated samples of a population cannot be normally distributed.
For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed.
RATIONALE
The Central Limit Theorem gives us information about the properties' sampling distributions of statistics to have given that the sample size is large enough. It tells us the sampling distribution's mean should be equal to the true population mean.
CONCEPT
Shape of a Sampling Distribution I need help with this question
9
The weekly salaries of full-time and part-time employees at a company are listed on the table.
What does the circled section represent?
Sixty-eight full-time employees earn $34 per week.
Two full-time employees earn more than $680 per week.
Thirty-four part-time employees earn more than $680 per week.
Two part-time employees earn between $680 and $690 per week.
RATIONALE
If we recall that the stem and leaf can give us the actual values in the data set, then the circle corresponds to
$683 and $684. We can then note that there are two part-time workers who make between $680 and $690.
CONCEPT
Stem-and-Leaf Plots
I need help with this question 10
In a survey to rate the customer service department of a company, 300 persons rated their agreement with the statement, "The staff is helpful and courteous." The information was put into a table.
Rating Frequency
Strongly Agree 32
Agree 50
Neutral 97
Disagree 53
Strongly Disagree 68
The relative frequency of people who strongly disagree with the statement is .
22.7%
10.7%
40.3%
68% [Show Less]