The average woman's height is 65 inches with a standard deviation of 3.5 inches. what proportion of women are shorter than 62inches tall

19.77%

Step-by-step explanation:

Given

Mean= μ=65 inches

SD= σ=3.5 inches

We have to find the proportion of women whose height is less than 62 inches.

For that we have to calculate z-score for the given value first. The z-score of a value tells us that how many standard deviations the value is far from mean. The area to the left of the z-score gives the proportion of data that is less than the z-score value and the area to the right gives the proportion.

So,

z-score of 62=  (x-μ )/σ

=(62-65)/3.5

=  (-3)/3.5

z-score of 62= -0.8571

To find the area to the left of the z-score, the z-score table is used which is easily available on the internet.

The area to the left of the z-score is 1.97662.

To find the proportion/percentage of women whose height is less than 62, the area has to be multiplied by 100.

Percentage of women whose height is less than 62 inches=0.197662*100

=19.77%

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?