The distribution of heights of a population of adults is approximately normal with mean 66 inches and SD 2.5 inches. [For those of you who are used to the metric system: one foot is 12 inches.] a. Approximately what percent of the adults are over 6 feet tall? Please don't enter the percent sign. b. Approximately what percent of the adults have heights that are within 1 inch of the average? Please don't enter the percent sign. c. Approximately what percent of the adults are 70 inches tall, to the nearest inch? Please don't enter the percent sign.

a. \[z=\frac{72-66}{2.5}=2.4\]Now look up the cumulative probability for z = 2.4 at this link and choosing 'normal.pdf'. http://www.math.bgu.ac.il/~ngur/Teaching/probability/ What value do you get?

0.9918

Correct. So the percentage of adults up to 6 feet tall is 99.18. Can you calculate the percentage over 6 feet tall?

Hint: 100% of the heights are under the normal distribution curve.

please answer only 30 minutes remain.

The percentage over 6 feet tall must be 100 - 99.18 = ?

0.82

Correct!

thanks b and c part

\[z=\frac{X-\mu}{\sigma}\] What are the z-scores for X = 65 and X = 67 ?

2

2.8

Not really. Do you know what values to use for mu and for sigma?

2.5

mu is the population mean = 66 sigma is the Standard deviation = 2.5 Can you calculate the z-scores using these values: \[z _{1}=\frac{65-66}{2.5}=?\] \[z _{2}=\frac{67-66}{2.5}=?\]

-0.4 and 0.4

Correct. Now if you look up the table at the link here http://www.math.bgu.ac.il/~ngur/Teaching/probability/ (select 'normal.pdf') what values of cumulative probability do you get for z = -0.4 and z = 0.4 ?

0.3446 and 0.6554

Now subtract the smaller value from the larger and multiply the result by 100 to find the required percentage for b.

31.08

Correct! For section c., I suggest finding the z-scores for X = 69 and X = 71, and then finding the cumulative probabilities for both. Next subtract the smaller probability from the larger and multiply the result by 100

1.2 and 2

0.8849 and 0.9772

answer is 9.23

correct or not

Good work! You are correct.

thanks

You're welcome :)

please help answer is wrong

@kropot72

please fast 3 min remain please urgent.

Then you need to recalculate using X = 69.5 and X = 70.5

1.4 and 1.8

0.9192 and 0.9641

4.49

correct or not

Correct!

thanks the answer is correct.

You're welcome :)

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