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 3.6% of the general population will live past their 90th birthday. In a graduating class of 738 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

Here the distribution is a binomial distribution with

probability of success = 3.6% = 0.036

sample size n = 738

if x is the number of general population that will live past their 90th birthday.

(a) Pr(x >=15) = 1 - BIN(x < 15 ; 738 ;0.036) = 1 - 0.0051 = 0.9949

(b) Pr(x >= 30) = 1 - BIN(x < 30 ; 738 ; 0.036) = 1 - 0.7256 = 0.2744

(c) Pr(25 <= x < = 35) = BINOMDIST(x <= 35 ; 38 ; 0.036) - BINOMDIST(x <25 ; 38 ; 0.036)

= 0.9564 - 0.4280

= 0.5284

(d) Pr(x>= 40) = 1 - BIN(x < 40 ; 738 ; 0.036) = 1 - 0.9922 = 0.0078

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