Question

The probability that you have 60 or fewer successes in 100 trials with p=0.5, is best calculated as:

a) P(XN<59.5; μ=50, σ2=25)

b) P(XN<60.5; μ=50, σ2=25)

c) P(XB≤59.5; n=100, p=0.5)

d) P(XB=60; n=100, p=0.5)

Answer 1

Using Binomial distribution, the probability that you have 60 or fewer successes in 100 trials is,

P(XB 60; n=100, p=0.5)

Using Normal approximation of Binomial distribution,

Mean μ= np = 100 * 0.5 = 50

σ2 = np(1-p) = 100 * 0.5 * (1 - 0.5) = 25

Using Continuity Correction Factor, probability that you have 60 or fewer successes in 100 trials

= P(XN 60) = P(XN < 60.5)

Thus, the correct answer is,

b) P(XN<60.5; μ=50, σ2=25)