Question

In studies for a medication, 88 percent of patients gained weight as a side effect. Suppose 476 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

(a) exactly 39 patients will gain weight as a side effect. (Round to four decimal places as needed)

(b) no more than 39 patients will gain weight as a side effect. (Round to four decimal places as needed)

(c) at least 48 patients will gain weight as a side effect. What does this result suggest? (Round to four decimal places as needed)

Answer #1

n= | 476 | p= | 0.0800 |

here mean of distribution=μ=np= | 38.08 |

and standard deviation σ=sqrt(np(1-p))= | 5.919 |

for normal distribution z score =(X-μ)/σx |

therefore from normal approximation of binomial distribution and continuity correction: |

a)

probability
=P(38.5<X<39.5)=P((38.5-38.08)/5.919)<Z<(39.5-38.08)/5.919)=P(0.07<Z<0.24)=0.5948-0.5279=0.0669 |

b)

probability
=P(X<39.5)=(Z<(39.5-38.08)/5.919)=P(Z<0.24)=0.5948 |

c)

probability
=P(X>47.5)=P(Z>(47.5-38.08)/5.919)=P(Z>1.59)=1-P(Z<1.59)=1-0.9441=0.0559 |

(since above is not less than 0.05 , getting 48 patients gaining weight as a side effect is not an unusual event.)

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