Question

A city reported that 54% of its adult residents have children. A researcher randomly samples 200 adult residents in the city and asks them whether or not they have children. (a) (2 points) How many adults in the sample are expected to have children? (b) (5 points) Verify the sampling distribution of the sample proportion is normal, and deter- mine the mean and standard deviation of the sampling distribution. (c) (3 points) What is the probability that 117 adults or more in the sample have children? x 0 1 2 3 4 5 6 P (x) 0.0041 0.0369 0.1382 0.2765 0.3110 0.1866 0.0467

Answer 1

This is a binomial distribution question with
n = 200
p = 0.54
q = 1 - p = 0.46
a) E(x) = n * p = 200 * 0.54 = 108
b) This binomial distribution can be approximated as Normal distribution since
np = 108 > 5 and nq = 92 > 5
Since we know that



The z-score at x = 116.5 is,

z = 1.2059
This implies that

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