1. Determine a data set you think would display a normal distribution. Be creati
ID: 3218445 • Letter: 1
Question
1. Determine a data set you think would display a normal distribution. Be creative!! Make sure to include why you feel the data follows a normal distribution. Remember that the normal distribution is for continuous data. (no examples involving height please!)
2. Estimate the sample mean and sample standard deviation of the normal distribution you are using.
3. Using the Empirical Rule and your mean and standard deviation from part 2, fill in the blanks in the following statement: 95% of the data falls between ________ and ________. Show your work.
Explanation / Answer
Part 1)
Here our variable is the average weight (lb) of male adults.
We collect 37 observations and our data set is as below:
Let the given variable is x,
X
157
160
167
150
157
140
153
152
160
164
161
151
154
152
159
149
147
152
160
164
161
151
154
152
161
151
154
152
159
149
151
154
152
159
149
147
152
The mean value is 154, the median is 153 and the mode is 152. They are close to each other. The data will follow approximately normal distribution.
Part 2)
We use excel to find the estimated mean and standard deviation:
Sample Mean
=AVERAGE(A2:A38)
= 154.5135
Sample Standard deviation
=STDEV(A2:A38)
= 5.6697
The estimated mean value is 154.5135
The estimated sample standard deviation 5.6697
Part 3)
According to empirical rule 95% data will lie in between of mean and 2 standard deviations.
145.5135 – (2*5.6697) and 145.5135 + (2*5.6697)
134.2 and 156.9
data falls between 134.2 lb and 156.9 lb
X
157
160
167
150
157
140
153
152
160
164
161
151
154
152
159
149
147
152
160
164
161
151
154
152
161
151
154
152
159
149
151
154
152
159
149
147
152
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