Question

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 = 300.

a.What is the probability of 190 to 200 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

b.What is the probability of 220 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

Answer 1

Let X be the given random variable.

It is given that it follows a binomial distribution with p = 0.70 and n = 300.

Thus, X ~ Binomial(n= 300, p = 0.70)

=> E(X) = n*p = 300*0.70 = 210

=> Var(X) = n*p*(1-p) = 300*0.70*0.30 = 63

Now, using the normal approximation of the binomial distribution, we get:

a.

The probability of getting 190 to 200 successes is given by:

b.

The probability of getting 220 or more successes is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.