Question

How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.4 lb of the population mean, and the population standard deviation is known to be 25 lb

Answer 1

147 women

Explanation:

From the statement we have, the error = 3.4 and the standard deviation sd = 25

Now, for 90% confidence, we have that a = 1 - 0.9 = 0.1

a / 2 = 0.05

if we look for the value of z for 0.05 (in the attached normal distribution table we look for), we have:

z_a / 2 = -1.645

Now we have to:

n = (z_a / 2 * sd / E) ^ 2

We replace and we are left with:

n = (-1,645 * 25 / 3.4) ^ 2

n = 146.3, that is to say 147 women.