# 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

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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,

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:

Step 3

The one, two and three standard deviations...

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