Question

If the probability of a newborn child being female is 0.5, find the probability that in 100 births, 55 or more will be female. Use the normal distribution to approximate the binomial distribution.

Answer 1

Mean = np

Standard deviation = √npq
Note: q = 1 - p

n = 100
p = 0.5
q = 0.5

Once you find the mean and standard deviation, use z-scores:
z = (x - mean)/sd
(x = 55)

Check a z-table to find the probability using the z-score you calculated.

Answer 2

54.5-50/50 = 4.5/5 = 0.9 z= 0.1841

Answer 3

I don't understand how mean got 54.5 or the equation 54.5-10/50 = 0.8 z=0.1841. I think mean (n)(p) = (100)(.5) = 50 standard deviation (p)(p)(q) square root = 5.