Question

According to National Health Survey, the heights of adult males in the United States are normally distributed with mean 69.0inches and standard deviation 2.8inches.

(a) Estimate the probability that a randomly chosen adult American male is between 66inches and 75inches tall.

(b) Estimate the percent of the adult American males that are taller than 6 feet 2inches.

Answer 1

hi

Answer 2

Do you know how to find the z-scores for 66 inches and 75 inches?

Answer 3

no sorry..

Answer 4

How are you expected to solve the question? Is it by using a statistical calculator or by using a standard normal distribution table?

Answer 5

by using a standard normal distribution table

Answer 6

The z-scores are found as follows:
\[z _{1}=\frac{X- \mu}{\sigma}=\frac{66-69}{2.8}\]
\[z _{2}=\frac{75-69}{2.8}\]
When you have calculated the z-scores I can show you how to use them on a standard normal distribution table.

Answer 7

don't even know what z-score is. can you explain more about it please?

Answer 8

i might need to use improper integrals ?

Answer 9

or probability

Answer 10

The z-score is needed when using standardised tables such as those for the normal distribution. The z-score is the standardised value of a random variable. Standardisation is performed by subtracting the population mean and dividing the result by the standard deviation. So the z-score is given by:
\[z=\frac{X- \mu}{\sigma}\]

Answer 11

ok so i got Z1= -1.0714 and Z2= 2.1428

Answer 12

and i don't know what to do next..

Answer 13

Use the table at the following link to find the cumulative probability for each of the z-scores. Then subtract the smaller probability value form the larger probability value to find the required probability.
http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

Answer 14

from*

Answer 15

@soobinkiki Can you find the probability values for z1 = -1.0714 and z2 = 2.1428 ?