# In a certain​ city, the average​ 20- to​ 29-year old man is 72.5 inches​ tall, with a standard deviation of 3.2 ​inches, while the average​ 20- to​ 29-year old woman is 64.5 inches​ tall, with a standard deviation of 3.8 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

We can use z scores to see which of the given values are relatively higher(taller) relative to their groups.

The 70-inch woman is relatively taller in women's group than 75-inch man in men's group (specified group).

How to get the z scores?

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have then it can be converted to standard normal distribution as

Using the above method to get the z scores for both the 75 inch man and 70 inch woman

Let X tracks height of men and Y tracks height of women, then we have:

Converting them to standard deviation and getting the z score:

For 75 inch man:

For 70 inch woman:

Thus,

The 70-inch woman is relatively taller in women's group than 75-inch man in men's group (specified group).

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​ 70-inch woman is taller.

Step-by-step explanation:

Given data:

For men

age group = 20 - 29 year

Height = 72.5 inches

standard deviation = 3.2 inches

For women

age group = 20 - 29 year

Height = 64.5 inches

standard deviation = 3.8 inches

To find:

who is taller?  a​ 75-inch man or a​ 70-inch woman?

To find that, firstly we find z- score for each gender.

Solve:

Z-score=(x-μ)/σ

where:

μ=mean

σ=std deviation

Z(men) = (75-72.5)/3.2

= 0.781

Z(women) = (70-64.5)/3.8

= 1.447

From the above, the z-score for the woman is relatively larger than that of the man, this means that the woman is taller.

## Related Questions

Your gym membership costs \$30 to join and \$25 per month. Which equation gives the total cost, y, for a membership that lasts x months?

(30+ 25)+(25 x 12) = then put your answer but this is my way of doing it.

Tell what whole number you can substitute for x in the following list so the numbers are ordered from least to greatest. 2/x ,x/6, 70%

Remark
Whole numbers are > 0.
Your choices are 1 2 3 4 5.
6 looks good but it won't work. The problem is that x / 6 = 1 if x = 6. Try it and see.

6/6 = 1
70% = 70/100 = 0.70 So whatever you use for x must give a result less than 0.7

So will five work? 5 / 6 = 0.8333. That's still too big. How about 4

4/6  = 2/3 = 0.666666667
That would work but does it work for 2/x

Yes it does
2/4 = 1/2 which is less than 2/3
Note than 3 will not work (why) nor will 2.

x = 4

6+2=8

8/2=4

2/4 =0.5  4/6=0.666 7/10=0.7

51=3k i do not get this can you help me please

51 = 3k. We can switch this around to 3k = 51 (because it's easier for me)

3k = 51.

We divide by 3 on both sides to just get "k".

3k / 3 = 51 / 3

k = 17.

3.78 divided by 0.9​

4.200

Step-by-step explanation:

Change the divisor 0.9 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

37.8 ÷ 9 = 4.200

and therefore:

3.78 ÷ 0.9 = 4.200

Both calculated to 3 decimal places.