Answer the following problems showing your work and explaining or analyzing your results

Question: #6196

Answer the following problems showing your work and explaining (or analyzing) your results.

1. The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?

99 34 86 57 73 85 91 93 46 96 88 79 68 85 89

2. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?

3. If you know the standard deviation, how do you find the variance?

4. To get the best deal on a stereo system, Louis called eight appliance stores and asked for the cost of a specific model. The prices he was quoted are listed below:

$216 $135 $281 $189 $218 $193 $299 $235

Find the standard deviation.

5. A company has 70 employees whose salaries are summarized in the frequency distribution below.

Salary

Number of Employees

5,001–10,000

10,001–15,000

15,001–20,000

20,001–25,000

25,001–30,000

Find the standard deviation.
Find the variance.

6. Calculate the mean and variance of the data. Show and explain your steps. Round to the nearest tenth.

14, 16, 7, 9, 11, 13, 8, 10

7. Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)

3, 5, 1, 6, 1, 2, 2, 6, 3, 4, 5, 1, 1, 3, 4, 2, 1, 6, 5, 3, 4, 2, 1, 3, 2, 4, 6, 5, 3, 1

8. Answer the following questions using the frequency distribution table you created in No. 7.

Which number(s) had the highest frequency?
How many times did a number of 4 or greater get thrown?
How many times was an odd number thrown?
How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?

9. The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the data below, find the following for each sample.

Range
Standard deviation
Variance

Lastly, compare the two sets of results.

Company

Wait times in seconds

Big Burger Company

105

120

175

115

120

The Cheesy Burger

133

124

200

101

147

118

125

10. What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?

Solution: #6202

Answer the following problems showing your work and explaining (or analyzing) your results

Answer the following problems showing your work and explaining (or analyzing) your results. The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean? 99 34 86 57 73 85 91 93 46 96 88 79 68 85 89 From the given data we can see that the sample mean is 77.93 and sample standard deviation is 19.03 so if the scores are within one standard deviation of the mean they should be in the interval (77.93-19.03, 77.93+19.03) = (58.9, 96.96) and we can see that 11 scores are in that interval. For 2 standard deviation of the mean the interval is = (77.93-2*19.03, 77.93+2*19.03) = (39.87, 115.99) and we can see that 14 scores are in that interval. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%? Note that, P(X>85) = P(Z>(85-74.8)/7.57)=P(Z> 1.35)=1-P(Z<1.35)= 1-0.9115=0.0885 So only 8.85% of the students has score over 85% thus the number of students = 15*0.0885=1.33. If you know the standard deviation, how do you find the variance? The variance of a distribution is nothing but the square of its standard deviation so if I know that standard deviation I would just square that to get the variance. To get the best deal on a stereo system, Louis called eight appliance stores and asked for the cost of a spec...