Please help !!! Need done asap

Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 c

Bogdan [553]

Answer:

a) 6.68% of heights less than 150 centimeters

b) 58.65% of heights between 160 centimeters and 180 centimeters

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 162, \sigma = 8$

a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{150 - 162}{8}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

6.68% of heights less than 150 centimeters

b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

X = 180

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{180 - 162}{8}$

$Z = 2.25$

$Z = 2.25$ has a pvalue of 0.9878

X = 160

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{160 - 162}{8}$

$Z = -0.25$

$Z = -0.25$ has a pvalue of 0.4013

0.9878 - 0.4013 = 0.5865

58.65% of heights between 160 centimeters and 180 centimeters

7 0

3 years ago

11 more than four times a number is 39

Aliun [14]

Hello!

Your answer is: 7

(X = "<em>A number</em>")

<em>"11 more than four times a number is 39"</em> in equation form is: 4X + 11 = 39

to solve, first subtract 11 from both sides:

4X = 28

then divide both sides by 4 to get:

X = 7

I hope this helps, and have a nice day!

4 0

3 years ago

It took the Farhats 85 minutes to drive 102 miles. If they this same driving rate, how long will it take them (in minu get to th

STALIN [3.7K]

Answer:

255 minutes

Step-by-step explanation:

306 can be subtracted by 102 a total of 3 times. We know that for every 102 miles = 85 minutes. So 85 * 3 = 255.

8 0

3 years ago

Find the unknown side length x.

Ganezh [65]

Answer:

x = $\sqrt{65}$

Step-by-step explanation:

The altitude of the triangle must equal 4 because it is a right triangle with another leg of 3 and a hypotenuse of 5 (reason is due to the pythagorean theorem)

Therefore, the triangle on the right has legs of 4 and 7 and, again, use the phythagorean theorem to find 'x' (the hypotenuse)

$4^{2}$ + $7^{2}$ = $x^{2}$