# 6.4: Review Questions

Difficulty Level: At Grade Created by: CK-12

Part A. For each question, circle the most appropriate answer.

1. If the standard deviation of a population is 6, the population variance is:
1. 2.44
2. 3
3. 6
4. 36
2. What is the population standard deviation of the following data values? \begin{align*}3.3 \qquad 2.9 \qquad 8.5 \qquad 11.5\end{align*}
1. 3.61
2. 4.17
3. 6.55
4. 13.52
3. Suppose data are normally distributed, with a mean of 100 and a standard deviation of 20. Between what 2 values will approximately 68% of the data fall?
1. 60 and 140
2. 80 and 120
3. 20 and 100
4. 100 and 125
4. The sum of all of the deviations about the mean of a set of data is always going to be equal to:
1. positive
2. the mode
3. the standard deviation total
4. 0
5. What is the population variance of the following data values? \begin{align*}40 \qquad 38 \qquad 42 \qquad 47 \qquad 35\end{align*}
1. 4.03
2. 4.51
3. 16.24
4. 20.34
6. Suppose data are normally distributed, with a mean of 50 and a standard deviation of 10. Between what 2 values will approximately 95% of the data fall?
1. 40 and 60
2. 30 and 70
3. 20 and 80
4. 10 and 95
7. Suppose data are normally distributed, with a mean of 50 and a standard deviation of 10. What would be the variance?
1. 10
2. 40
3. 50
4. 100
8. If data are normally distributed, what percentage of the data should lie within the range of \begin{align*}\mu \pm 3\sigma\end{align*}?
1. 34%
2. 68%
3. 95%
4. 99.7%
9. If a normally distributed population has a mean of 75 and a standard deviation of 15, what proportion of the values would be expected to lie between 45 and 105?
1. 34%
2. 68%
3. 95%
4. 99.7%
10. If a normally distributed population has a mean of 25 and a standard deviation of 5.5, what proportion of the values would be expected to lie between 19.5 and 30.5?
1. 34%
2. 68%
3. 95%
4. 99.7%

Part B. Answer the following questions and show all work (including diagrams) to create a complete answer.

1. In the United States, cola can normally be bought in 8 oz cans. A survey was conducted where 250 cans of cola were taken from a manufacturing warehouse and the volumes were measured. It was found that the mean volume was 7.5 oz, and the standard deviation was 0.1 oz. Draw a normal distribution curve to represent this data and then answer the following questions. (b) 68% of the volumes can be found between __________ and _________. (c) 95% of the volumes can be found between __________ and _________. (d) 99.7% of the volumes can be found between __________ and _________.
2. The mean height of the fourth graders in a local elementary school was found to be 4’8”, or 56”. The standard deviation was found to be 5”. Draw a normal distribution curve to represent this data and then answer the following questions. (b) 68% of the heights can be found between __________ and _________. (c) 95% of the heights can be found between __________ and _________. (d) 99.7% of the heights can be found between __________ and _________.
3. The following data was collected: \begin{align*}5 \qquad 8 \qquad 9 \qquad 10 \qquad 4 \qquad 3 \qquad 7 \qquad 5\end{align*} Fill in the chart below and calculate the standard deviation and the variance.
Data \begin{align*}(x)\end{align*} Mean \begin{align*}(\mu)\end{align*} Data \begin{align*}-\end{align*} Mean \begin{align*}(x - \mu)\end{align*} Square of Data \begin{align*}-\end{align*} Mean \begin{align*}(x-\mu)^2\end{align*}
\begin{align*}\sum\end{align*}
1. The following data was collected. \begin{align*}11 \qquad 15 \qquad 16 \qquad 12 \qquad 19 \qquad 17 \qquad 14 \qquad 18 \qquad 15 \qquad 10\end{align*} Fill in the chart below and calculate the standard deviation and the variance.
Data \begin{align*}(x)\end{align*} Mean \begin{align*}(\mu)\end{align*} Data \begin{align*}-\end{align*} Mean \begin{align*}(x - \mu)\end{align*} Square of Data \begin{align*}-\end{align*} Mean \begin{align*}(x-\mu)^2\end{align*}
\begin{align*}\sum\end{align*}
1. Mrs. Meery has recorded her exam results for the current mathematics exam. The results are shown below: \begin{align*}& 64 \quad 98 \quad 78 \quad 76 \quad 56 \quad 48 \quad 89 \quad 78 \quad 69 \quad 90 \quad 89\\ & 97 \quad 67 \quad 58 \quad 59 \quad 50 \quad 78 \quad 89 \quad 68 \quad 83 \quad 72 \quad 91\end{align*} (b) Determine the mean for this data. (c) Determine the standard deviation for this data. (d) Determine the variance for this data. (e) Draw a normal distribution curve to represent the data Mrs. Meery found in her class.
2. Mrs. Landry decided to do the same analysis as Mrs. Meery for her math class. She has recorded her exam results for the current mathematics exam. The results are shown below: \begin{align*}& 89 \quad 87 \quad 81 \quad 84 \quad 76 \quad 72 \quad 67 \quad 49 \quad 55 \quad 38 \quad 67 \quad 90 \quad 59\\ & 87 \quad 89 \quad 69 \quad 92 \quad 90 \quad 79 \quad 84 \quad 69 \quad 93 \quad 85 \quad 70 \quad 87 \quad 80\end{align*} (b) Determine the mean for this data. (c) Determine the standard deviation for this data. (d) Determine the variance for this data. (e) Draw a normal distribution curve to represent the data Mrs. Landry found in her class.
3. 200 senior high students were asked how long they had to wait in the cafeteria line for lunch. Their responses were found to be normally distributed, with a mean of 15 minutes and a standard deviation of 3.5 minutes. Copy the following bell curve onto your paper and answer the questions below. (b) How many students would you expect to wait more than 11.5 minutes? (c) How many students would you expect to wait more than 18.5 minutes? (d) How many students would you expect to wait between 11.5 and 18.5 minutes?
4. 350 babies were born at Neo Hospital in the past 6 months. The average weight for the babies was found to be 6.8 lbs, with a standard deviation of 0.5 lbs. Copy the following bell curve onto your paper and answer the questions below. (b) How many babies would you expect to weigh more than 7.3 lbs? (c) How many babies would you expect to weigh more than 7.8 lbs? (d) How many babies would you expect to weigh between 6.3 and 7.8 lbs?
5. Sudoku is a very popular logic game of number combinations. It originated in the late 1800's by the French press, Le Siècle. The average times (in minutes) it takes those in a senior math class to complete a Sudoku puzzle are found below. Draw a normal distribution curve to represent this data. Determine what time a student must complete a Sudoku puzzle in to be in the top 0.13%. \begin{align*}& 20 \quad 15 \quad 21 \quad 24 \quad 7 \quad \ 19 \quad 10 \quad 17 \quad 15 \quad 22 \quad 31 \quad 19 \quad 20 \quad 21\\ & 21 \quad \ 9 \quad 12 \quad 26 \quad 24 \quad 28 \quad 19 \quad 16 \quad 24 \quad 11 \quad 17 \quad 31 \quad 25 \quad 13\\ & 16 \quad 18 \quad 22 \quad 32 \quad 9 \quad \ 15 \quad 19 \quad 27 \quad 14 \quad 25 \quad 32 \quad 29 \quad \quad \end{align*}
6. Sheldon has planted seedlings in his garden in the back yard. After 30 days, he measures the heights of the seedlings to determine how much they have grown. The differences in heights can be seen in the table below. The heights are measured in inches. Draw a normal distribution curve to represent the data. Determine what the range of the differences in heights of the seedlings is for the middle 68% of the data. \begin{align*}& 10 \quad 3 \quad 8 \quad 4 \quad \ \ 7 \quad 12 \quad 8 \quad \ 5 \quad 4 \quad \ 9 \quad \ 3 \quad 8\\ & 6 \quad 10 \quad 7 \quad 10 \quad 11 \quad 8 \quad 12 \quad 9 \quad 10 \quad 7 \quad 8 \quad 11\end{align*}

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