Question

Suppose that x has a binomial distribution with n = 50 and p = .6, so that μ = np = 30 and σ = np(1 − p) = 3.4641. Calculate the following probabilities using the normal approximation with the continuity correction. (Hint: 26 < x < 36 is the same as 27 ≤ x ≤ 35. Round your answers to four decimal places.)

(a)    P(x = 30)

(b)    P(x = 26)

(c)    P(x ≤ 26)

(d) P(26 ≤ x ≤ 36)

(e)    P(26 < x < 36)

Answer 1

n = 50
p = 0.6, q = 0.4
μ = np = 30 and σ = np(1 − p) = 3.4641

binomial distribution formula gives

a) P(X=30) = 0.1146

b) P(X=26) = 0.0584

c)

d)

e)