You may need to use the appropriate appendix table or technology to answer this question.
Assume a binomial probability distribution has
p = 0.70
and n = 400.
(a)
What are the mean and standard deviation? (Round your answers to two decimal places.)
mean standard deviation
(b)
Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.
(c)
What is the probability of 260 to 270 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
(d)
What is the probability of 290 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
(e)
What is the advantage of using the normal probability distribution to approximate the binomial probabilities?
How would you calculate the probability in part (d) using the binomial distribution. (Use f(x) to denote the binomial probability function.)
P(x ≥ 290) = f(0) + f(1) + + f(289) + f(290)
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Assume a binomial probability distribution has p = 0.70 and n = 400.
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