The question is –
Among American women aged 20 to 29 years, 10% are less than 60.8
inches tall, 80% are between 60.8 and 67.6 inches tall, and 10% are
more than 67.6 inches tall.17 Assuming that the height distribution
can adequately be approximated by a normal curve, find the mean and
standard deviation of the distribution.
I know I can find the mean with (60.8+67.6)/2 = 64.2
I am just not sure on how to find the standard deviation with the given percentages. If the percentages were ~ 68, 95, or 99.7 I think I could figure it out
Best Answer
After some research and help from a friend, I realized my professor decided never to give us a z-score table.
Because 67.6 is greater than 90% of the population, search for the value that is closest to .9 on the chart above, in this case, .8997 which would give us a z-score of 1.28
since 𝜎 = (x - μ) / z -> (67.6 - 64.2) / 1.28 = 2.65625
the standard deviation (𝜎) is 2.65625