Question

# Suppose we have a binomial distribution with n trials and probability of success p. The random...

Suppose we have a binomial distribution with n trials and probability of success p. The random variable r is the number of successes in the n trials, and the random variable representing the proportion of successes is = r/n.

(a) n = 44; p = 0.53; Compute P(0.30 ≤ ≤ 0.45). (Round your answer to four decimal places.)

(b) n = 36; p = 0.29; Compute the probability that will exceed 0.35. (Round your answer to four decimal places.)

(c) n = 41; p = 0.09; Can we approximate by a normal distribution? Explain.

---Select--- Yes No ,   ---Select--- can cannot be approximated by a normal random variable because

#### Homework Answers

Answer #1

(a) Given : n = 44,  p = 0.53

Now ,

; From standard normal distribution table

(b) Given : n=36 , p=0.29

Now ,

; From standard normal distribution table

(c) Given : n=41 ,p=0.09

Here , np=41*0.09=3.69<5

Therefore , we cannot be approximated by a normal random variable because np<5

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