Mathematics – Statistics Week 4_Assignment_USING THE NORMAL DISTRIBUTION AND CONFIDENCE INTERVALS
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USING THE NORMAL DISTRIBUTION AND CONFIDENCE INTERVALS
Instructions:
1. This Assignment will make use of the data set created in Week 1 – See attached excel document.
2. Use the attached word document to complete this week assignment.
Part 1: Using the Normal Distribution
Given that BMI is approximately normally distributed, present the following summary statistics for BMI of smokers and nonsmokers in the table below.
Smokers 
Nonsmokers 

Mean 

Standard Deviation 

Sample size ( 
Use this table to answer the following questions based on your individual data. Compute probabilities based on the normal distribution. For each portion write a 1sentence explanation as to how Excel was used to assist you in your computations.
1. Find the percent of smokers expected to have a BMI of greater than 25 (overweight).
2. Find the percent of nonsmokers expected to have a BMI of less than 18.5 (underweight).
3. A normal BMI range is between 18.5 and 24.9. What percentage of smokers are expected to be within this range? What percentage of nonsmokers are expected to be within this range?
4. A researcher is interested in which BMI represents the 90th percentile (where 90% are at this BMI level or lower). What BMI score represents the 90th percentile cutoff rate?
Part 2: Creating Confidence Intervals
Using the information from Part 1 (above), calculate a 90%, 95%, and 99% confidence interval for both groups. Then, complete the following table:
Group 
90% Confidence Interval 
95% Confidence Interval 
99% Confidence Interval 
Smokers 

Nonsmokers 
Use this table to answer the following questions based on your individual data.
1. As the level of confidence increases, what happens to the width of the confidence interval? Does it increase or decrease? Explain one (1) reason why this would happen.
2. Using the 95% confidence interval, compare the BMI of smokers versus nonsmokers. Write a 2 to 3sentence paragraph explaining if these intervals overlap or not. What does the comparison indicate regarding the differences in BMI between the two groups?
3. Explain, in 1–2 sentences, one situation in which you (as a researcher) may choose a 99% confidence interval? A 90% interval? Fully justify your choice.
Week 4 Project Assignment:
Using the Normal Distribution and Confidence Intervals
Prepared by: Ligia Rivera
Date: June 25, 2023
Page 2 of 2
Part 1: Using the Normal Distribution
Open the “BODY DATA” file created in the Week 1 Discussion. Use it to address the following:
Given that BMI is approximately normally distributed, present the following summary statistics for BMI of “Smokers” and “Nonsmokers” in the table below.
Smokers 
Nonsmokers 

Mean 

Standard deviation 

Sample size ( 
1) Find the percent of smokers expected to have a BMI of greater than 25 (overweight).
2) Find the percent of nonsmokers expected to have a BMI of less than 18.5 (underweight).
3) A normal BMI range is between 18.5 and 24.9. What percentage of smokers are expected to be within this range? What percentage of nonsmokers are expected to be within this range?
4) A researcher is interested in which BMI represents the 90th percentile (where 90% are at this BMI level or lower). What BMI score represents the 90th percentile cutoff rate?
Part 2: Creating Confidence Intervals
Using the information from Part 1 (above), calculate a 90%, 95%, and 99% confidence interval for both groups. Then, complete the following table:
Group 
90% Confidence Interval 
95% Confidence Interval 
99% Confidence Interval 
Smokers 



Nonsmokers 



Use this table to answer the following questions based on your individual data.
Note: Replace the questions (below) with your responses.
1. As the level of confidence increases, what happens to the width of the confidence interval? Does it increase or decrease? Explain one reason why this would happen.
2. Using the 95% confidence interval, compare the BMI of smokers versus nonsmokers. Write a 2 to 3sentence paragraph explaining if these intervals overlap or not. What does the comparison indicate regarding the differences in BMI between the two groups?
3. Explain, in 1–2 sentences, one situation in which you (as a researcher) may choose a 99% confidence interval? A 90% interval? Fully justify your choice.
Sheet1
AGE  Smoker  PULSE  HDL  LDL  WEIGHT  HEIGHT  BMI  Region  SYSTOLIC  BMI SMOKERS  BMI NONSMOKERS  
68  0  90  95  113  45.2  151.6  19.7  4  132  28.1  19.7  
51  0  94  71  98  150.4  159.7  59.0  2  120  37.0  59.0  
18  0  68  62  97  71.5  158.4  28.5  2  120  36.5  28.5  
18  0  90  66  76  74.0  173.6  24.6  3  106  23.1  24.6  
20  0  82  78  140  64.0  160.1  25.0  2  110  20.2  25.0  
45  0  80  45  112  92.8  164.8  34.2  1  146  29.6  34.2  
51  0  74  47  112  85.9  172.1  29.0  4  128  24.9  29.0  
63  0  56  52  121  105.5  153.2  45.0  2  156  19.9  45.0  
80  0  100  65  120  43.3  134.5  23.9  1  122  25.8  23.9  
59  0  74  63  119  114.9  169.1  40.2  3  124  26.0  40.2  
33  0  76  45  111  89.1  160.2  34.7  1  108  33.7  34.7  
60  0  76  86  95  58.5  157.8  23.5  2  136  23.4  23.5  
38  0  86  49  85  57.2  166.3  20.7  4  112  32.7  20.7  
68  0  74  57  135  81.4  158.4  32.4  1  136  26.8  32.4  
21  0  66  63  146  95.6  177.8  30.2  3  112  18.1  30.2  
37  0  62  65  148  86.5  152.4  37.2  3  110  21.3  37.2  
69  0  78  47  96  79.1  164.1  29.4  3  142  23.9  29.4  
46  0  68  56  143  68.4  160.6  26.5  4  112  25.2  26.5  
41  0  62  46  75  85.7  167.7  30.5  4  102  22.8  30.5  
80  0  62  62  104  50.4  158.8  20.0  1  130  29.7  20.0  
41  0  74  61  180  72.1  156.5  29.4  2  98  31.2  29.4  
68  0  104  68  99  77.2  157.6  31.1  3  140  44.2  31.1  
42  0  54  66  76  83.3  169.7  28.9  2  126  29.3  28.9  
64  0  74  61  121  88.6  155.0  36.9  2  120  31.6  36.9  
33  0  74  40  85  84.6  170.6  29.1  1  114  35.0  29.1  
63  0  84  64  98  81.0  160.1  31.6  1  114  27.1  31.6  
60  0  60  81  99  53.5  156.4  21.9  1  186  29.6  21.9  
35  1  54  68  100  84.1  172.9  28.1  4  126  
44  1  66  40  122  112.8  174.6  37.0  3  128  
37  1  56  57  71  123.9  184.3  36.5  2  114  
80  1  80  47  58  76.5  182.0  23.1  3  96  
18  1  72  47  87  71.7  188.4  20.2  3  120  
62  1  64  43  79  90.0  174.3  29.6  3  136  
41  1  64  63  133  70.6  168.5  24.9  2  106  
36  1  96  97  251  64.8  180.3  19.9  2  114  
80  1  58  34  69  76.6  172.2  25.8  1  136  
55  1  66  63  63  93.7  189.7  26.0  2  120  
32  1  58  58  140  107.4  178.5  33.7  1  122  
27  1  58  39  86  74.6  178.7  23.4  2  120  
62  1  68  26  122  106.0  180.0  32.7  1  142  
24  1  70  62  144  84.4  177.5  26.8  2  120  
19  1  84  41  69  59.6  181.3  18.1  3  108  
80  1  58  74  182  63.4  172.6  21.3  3  160  
27  1  78  65  158  70.4  171.5  23.9  4  118  
62  1  66  44  72  69.9  166.4  25.2  1  108  
35  1  86  46  126  63.7  167.1  22.8  1  120  
24  1  70  47  104  90.2  174.2  29.7  3  106  
28  1  54  39  123  99.4  178.6  31.2  3  128  
58  1  84  36  118  127.8  170.0  44.2  1  128  
18  1  72  60  84  88.3  173.5  29.3  3  128  
46  1  74  42  153  94.6  173.1  31.6  3  138  
45  1  64  45  167  119.8  185.1  35.0  4  116  
27  1  66  49  146  78.8  170.5  27.1  3  112  
69  1  62  35  84  84.4  169.0  29.6  1  120 
Sheet2
Sheet3
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