Use the normal approximation to the binomial to find that probability for the specific value of X. n = 30, p = 0.4, X = 5?
- stanschimLv 72 weeks ago
The probability of a specific value of the normal distribution is 0. In order to use it to approximate the binomial distribution, we will need to consider a range of values, say from 4.5 to 5.5 and compute the probability over the range.
The mean of the binomial distribution = np = 30(0.4) = 12
The variance of the binomial distribution = np(1-p) = 30(0.4)(0.6) = 7.2
The standard deviation is the square root of the variance = 2.68
Lower z score = (4.5 - 12) / 2.68 = -2.80
Upper z score = (5.5 - 12) / 2.68 = -2.43
P(Z between these values) = about 0.005.