A business center is 3.75 times as tall as a monument. The monument is 444 feet tall. About how tall is the business center

To help students improve their reading, a school district decides to implement a reading program. It is to be administered to th

Crank

Answer:

a) $P(X>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140-122}{18})=P(Z>1)$

And we can find this probability using the complement rule and the normal standard table or excel and we got:

$P(Z>1)=1-P(Z$

b) $z=-1.036$

And if we solve for a we got

$a=122 -1.036*18=103.35$

So the value of height that separates the bottom 15% of data from the top 85% is 103.35.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(122,18)$

Where $\mu=122$ and $\sigma=18$

We are interested on this probability

$P(X>140)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140-122}{18})=P(Z>1)$

And we can find this probability using the complement rule and the normal standard table or excel and we got:

$P(Z>1)=1-P(Z$

Part b

For this part we want to find a value a, such that we satisfy this condition:

$P(X$ (a)

$P(X>a)=0.85$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.15 of the area on the left and 0.85 of the area on the right it's z=-1.036. On this case P(Z<-1.036)=0.15 and P(z>-1.036)=0.85

If we use condition (b) from previous we have this:

$P(X$