Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x

Question

Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x < 48).
A)0.3015
B)0.0094
C)0.0054
D)0.4946

Quizplus · Accepted Answer

Using the normal approximation, the mean μ = np = 60 and the standard deviation σ = √(np(1-p)) = √(24) ≈ 4.899. Applying the continuity correction, P(x < 48) becomes P(x ≤ 47.5). The z-score is (47.5 - 60) / 4.899 ≈ -2.55. Using the standard normal distribution table, P(z < -2.55) ≈ 0.0054.

Assume That X Is a Binomial Random Variable with N