SOLUTION: Suppose that the variable X is normally distributed with a mean of 200 and a standard deviation of 25. (i) What proportion of X-values lies between 180 and 205? (ii) Below wha

Question 301727: Suppose that the variable X is normally distributed
with a mean of 200 and a standard deviation of 25.
(i) What proportion of X-values lies between 180 and
205?
(ii) Below what value do 30 per cent of X-values lie?

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Find the z score for 180 and 205.

Now lookup the area under the curve for each z score (NORMDIST in EXCEL).

The difference in those is the area of interest to us.

So almost 37% lies between 180 and 205.
.
..
The z score for 187 is 0.3015.
The z score for 186 is 0.2877.
The z score for 186.9 is 0.3001.

RELATED QUESTIONS
For a normally distributed variable with a mean of 10 and standard deviation of 5, what... (answered by mathmate)

For a normally distributed variable with a mean of 10 and standard deviation of 5, what... (answered by fractalier)

For a normally distributed variable with a mean of 10 and standard deviation of 5, what... (answered by robertb)

suppose it is known that in certain large human population cranial length is normally... (answered by ewatrrr)

X is a normally distributed random variable with a mean of 22 and a standard deviation of (answered by stanbon)

A random variable X is normally distributed with a mean of 85 and a standard deviation of (answered by ewatrrr)

Assume that the random variable X is normally distributed with a mean of 70 and a... (answered by rothauserc)

Given that x is a normally distributed random variable with a mean of 28 and a standard... (answered by stanbon)