A public opinion poll in Southern California was conducted todetermine whether S

Question

A public opinion poll in Southern California was conducted todetermine whether Southern Californians are prepared for the bigearthquake that experts predict will devistate the region sometimein the next 50 years. It was learned that 60% have notsecured objects in their homes that might fall and cause injury anddamage during a tremblor. In a random sample of n=864Southern Californians, Let X equal the number who have not securedobjects in their homes. Find , approximately. P(496 leq X leq 548), approximately.

Explanation / Answer

We can use the Central Limit Theorem to approximate the binomialdistribution to normal. Let Y be the normally distributed random variable of number ofSouthern Californians who have not secured objects in theirhomes.       X~Bin(864, 0.6) ˜Y~Nor(864*0.6, 864*0.6*[1-0.6])                              ˜ Y~Nor(518.4, 207.36) P(496

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