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 can, 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.

A survey of adults found that 8% say their favorite sport is auto racing. You randomly select 300 adults and ask them to name their favorite sport. Complete parts (a) through (d).

(b) Find the probability that the number of people who say auto racing is their favorite sport is more than 33.

Explanation / Answer

Binomial distribution can be used to approximate anormal distribution with parametrs n and p. The normal approximation is N(np, sqrt(np(1-p)).

Thus the z value for 33, is (33-300*0.08)/sqrt(0.08*0.92*300)=1.279, thus the normal probability P(x>33)=10%.

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