Question

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

Answer #1

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<X<37.5)=P((36.5-30)/3.873)<Z<(37.5-30)/3.873) |

=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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