Normal DistributionsExample: Delta reports that the average age of their pilots is 42.6 years with a standard deviation of 6.3 years.Assume that the distribution of ages is normally distributed.Draw and label the normalmodel which describes theages of Delta pilots.M+l0=42.6+6.3=48.9M-lo=42.6- 6.3= 36. 3%3D%3DM+20=48.9+6.3= 55.2M+30=55.2+6.33 61.5M-20=36.3-6.334%З4/.342= 30M-30=30-6.368%= 23.713.5-113.5%.95%2.35%2.35%0.I57.0.15%99.7%Let's receStandard50 years is oftheinWhat percentage of Delta pilots is older than 50? Why can we not use the Empirical Rule to arrive at an exactanswer to this question? What is the best we can say?How willg the chserthen 5061.542.636.33023.7ALL

Question
Asked Jan 13, 2020
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Normal Distributions
Example: Delta reports that the average age of their pilots is 42.6 years with a standard deviation of 6.3 years.
Assume that the distribution of ages is normally distributed.
Draw and label the normal
model which describes the
ages of Delta pilots.
M+l0=42.6+6.3
=48.9
M-lo=42.6- 6.3
= 36. 3
%3D
%3D
M+20=48.9+6.3
= 55.2
M+30=55.2+6.3
3 61.5
M-20=36.3-6.3
34%
З4/.
342
= 30
M-30=30-6.3
68%
= 23.7
13.5-1
13.5%.
95%
2.35%
2.35%
0.I57.
0.15%
99.7%
Let's rece
Standard
50 years is of
the
in
What percentage of Delta pilots is older than 50? Why can we not use the Empirical Rule to arrive at an exact
answer to this question? What is the best we can say?
How will
g the chser
then 50
61.5
42.6
36.3
30
23.7
ALL
help_outline

Image Transcriptionclose

Normal Distributions Example: Delta reports that the average age of their pilots is 42.6 years with a standard deviation of 6.3 years. Assume that the distribution of ages is normally distributed. Draw and label the normal model which describes the ages of Delta pilots. M+l0=42.6+6.3 =48.9 M-lo=42.6- 6.3 = 36. 3 %3D %3D M+20=48.9+6.3 = 55.2 M+30=55.2+6.3 3 61.5 M-20=36.3-6.3 34% З4/. 342 = 30 M-30=30-6.3 68% = 23.7 13.5-1 13.5%. 95% 2.35% 2.35% 0.I57. 0.15% 99.7% Let's rece Standard 50 years is of the in What percentage of Delta pilots is older than 50? Why can we not use the Empirical Rule to arrive at an exact answer to this question? What is the best we can say? How will g the chser then 50 61.5 42.6 36.3 30 23.7 ALL

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Expert Answer

Step 1

68-95-99.7-rule:

Let X be an observation from a normal distribution, having mean µ and standard deviation σ, then according to the 68-95-99.7-rule, approximately 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean respectively. That is,

Statistics homework question answer, step 1, image 1
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Step 2

The percentage of Delta pilots is greater than 50:

The random variable follows normal distribution with mean 42.6 and standard deviation 6.3. The required probability is calculated as follows:

Statistics homework question answer, step 2, image 1
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Step 3

The one, two and three standard deviations...

Statistics homework question answer, step 3, image 1
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