In the following problem, check that it is appropriate to use the normal approxi

Question

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.9% of the general population will live past their 90th birthday. In a graduating class of 742 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday


(b) 30 or more will live beyond their 90th birthday


(c) between 25 and 35 will live beyond their 90th birthday


(d) more than 40 will live beyond their 90th birthday

Explanation / Answer

Mean= 742 x .039 => 28.938

Find the Standard Deviation.
Standard Deviation= (742 x .039 x .963) = 27.864 => 5.27

A) 15 or more
(14.5-28.938)/5.27 = -2.73 -> .0052
Take 1- .0052 = .9948

B) 30 or more
(29.5-28.938)/5.27 = .1066 -> .4331
Take 1- .4331 = .5669

C) Between 25 and 35
((35.5-28.938)/5.27) - ((24.5-28.938)/5.27) =
1.245 - -.84 => 2.08

D) More than 40
(40.5-28.938)/5.27 = 2.19 -> .9932
Take 1- .9932 = .0068

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