Question

A binomial experiment consists of 800 trials. The probability of success for each trial is 0.4. What is the probability of obtaining 300?-325 ?successes? Approximate the probability using a normal distribution.? (This binomial experiment easily passes the? rule-of-thumb test for approximating a binomial distribution using a normal? distribution, as you can check. When computing the? probability, adjust the given interval by extending the range by 0.5 on each? side.)

Answer 1

Let X be a random variable follows binomial distribtuion

X ~Binomial(800, 0.4)

The normal approximation to binomial distribution :

and

Hence, it is appropriate to use normal approximation

Therefore

Therefore X ~N(320,13.86)

= 0.4207+0.1554 =0.5761

Answer: Prob = 0.5761