Question

In studies for medication, 11 percent of patients gained weight as a side effect. Suppose 402 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

a) exactly 45 patients gain weight as a side effect

b) no more than 45 patients will gain weight as a side effect

c) at least 53 patients will gain weight as a side effect. What does this result suggest?

Answer #1

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**Answer:**

n= | 402 | p= | 0.1100 | |

here mean of distribution=μ=np= | 44.22 | |||

and standard deviation σ=sqrt(np(1-p))= | 6.2734 | |||

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

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

a)

probability = | P(44.5<X<45.5) | = | P(-0.0446<Z<0.2040)= | 0.0630 |

b)

probability = | P(X<45.5) | = | P(Z<0.2040)= | 0.5808 |

c)

probability = | P(X>52.5) | = | P(Z>1.319858)= | 0.0934 |

as the probability of this event is significant low, therefore this may indciate that percentage is lower than 11%

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