If x is a binomial random variable where n = 100 and p = 0.30, find the probability that x is greater than or equal to 35 using the normal approximation to the binomial. (Discuss whether continuity correction is required or not)
Solution :
Given that,
Using binomial distribution,
= n * p = 100 *9 0.30 = 30
= n * p * q = 100 * 0.30 * 0.70 = 2.5826
Using continuity correction ,
P(x 34.5) = 1 - P(x 34.5)
= 1 - P((x - ) / < (34.5 - 30) / 2.5826)
= 1 - P(z < 1.74)
= 0.0409
continuity correction is required .
If x is a binomial random variable where n = 100 and p = 0.30, find...
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