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 p̂ = r/n.
(a) n = 44; p = 0.53; Compute P(0.30
≤ p̂ ≤ 0.45). (Round your answer to four decimal
places.)
(b) n = 36; p = 0.29; Compute the probability
that p̂ will exceed 0.35. (Round your answer to four
decimal places.)
(c) n = 41; p = 0.09; Can we approximate
p̂ by a normal distribution? Explain.
---Select--- Yes No , p̂ ---Select--- can cannot be approximated by a normal random variable because
(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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