Decide whether you can use the normal distribution to approximate the binomial d

Question

Decide whether you can use the normal distribution to approximate the binomial distribution. If you ca, use the normal distribution to approximate the indicated probabilities and sketch their graphs if you cannot, explain why and use the binomial distribution to find the indicated probabilities. Five percent in use public transportation to get to work. You randomly select279 workers and ask them if they use public transportation to get to work. Complete parts (a) through (d). A transit authority offers discount rates to companies that have at least 30 employees who use Public transportation to get to work. There are 491 employees in a company. What is the probability that the company will not get the discount? Can the normal distribution be used to approximate the binomial distribution? A. Yes, because both np 5 and nq 5. B. No, because nq

Explanation / Answer

here p=0.05 and n=491

hence mean =np=24.55

and std deviation =(np(1-p))1/2 =4.8293

therefore probabilty that company will not get discount =P(X<30) =P(Z<(29.5-24.55)/4.8293)

              =P(Z<1.025)=0.8473

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