Question

I need QUESTIONS 1 , 2 AND 3 !

The overhead reach distances of adult females are normally distributed with a mean of

200 cm and a standard deviation of 8.9 cm.

a. Find the probability that an individual distance is greater than 212.50cm

.b. Find the probability that the mean for 20 randomly selected distances is greater than 198.20 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

Question #1 Part A. The probability is ___ ?

​(Round to four decimal places as​ needed.)

Question #2 Part B. The probability is ___ ?

​(Round to four decimal places as​ needed.)

Question #3 Part C. Choose the correct answer below.

A.The normal distribution can be used because the probability is less than 0.5

B.The normal distribution can be used because the mean is large.

C.The normal distribution can be used because the original population has a normal distribution.

D.The normal distribution can be used because the finite population correction factor is small.

Answer 1

Here distribution is normal with mean=200 and standard deviation=8.9

a. We need to find

As distribution is normal we can convert x to z

Here we have find P(0<z<1.40) using below table

b. Now we need to find , as population is normal sample mean is also normal as per central limit theorem

c. As population is normal we can use normal distribution as per central theorem

So answer here is

C.The normal distribution can be used because the original population has a normal distribution.