Question

# Compute​ P(X) using the binomial probability formula. Then determine whether the normal distribution can be used...

Compute​ P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If​ so, approximate​ P(X) using the normal distribution and compare the result with the exact probability.

n=60​, p=0.5 and X=37

A. find P(X)

B. find P(x) using normal distribution

C. compare result with exact probability

a)

here this is binomial with parameter n="60 and p=0.5

 P(X=37)= (60C37)0.537(1−0.5)(60-37)    = 0.0203

b)

 here mean of distribution=μ=np= 30.00 and standard deviation σ=sqrt(np(1-p))= 3.87 for normal distribution z score =(X-μ)/σx
 therefore from normal approximation of binomial distribution and continuity correction:
 probability P(X=37) =P(36.5

=P(1.68<Z<1.94)=0.9738-0.9535=0.0203

c)

both result are approximately the same till 4th decimal places

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