I need a little help with the formulas here. I’m not sure if I am doing this right.
Records show that 29% of all payments to a mail-order company are submitted after the due date. Suppose that 50 payments are submitted this week. Let x be a random variable that represents that number of payments that are late.
a. Is the normal approximation to the binomial appropriate for this problem? Why?
n=50, p=.29, q=.71
np= 50(.29)= 14.5, np= 50(.71)= 35.5
Normal approximation by a normal random variable is appropriate because both np and nq exceed 5.
b. Estimate P(x ≥ 18)
µ= p= 0.29, σ= √(p)(q)/n = √(.29)(.71)/50 = 0.06
Continuity Correction: 0.5/50 = 0.01
P(x ≥ 18-0.01)
P(z ≥ (0.179 - 0.29)/0.06) = -1.85
P(z ≥ -1.85) = 0.0322