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irga5000 [103]
2 years ago
13

The heights of the men age 18 and over in HANES5 averaged 69 inches; the SD was 3 inches. Suppose the histogram of their heights

follows the normal curve. Such a man that is 6 feet tall is at the percentile of this height distribution. (Enter the nearest whole number.) What is the 25th percentile, to the nearest inch
Mathematics
1 answer:
emmasim [6.3K]2 years ago
7 0

Answer:

a) 84th percentile.

b) The 25th percentile is of 67 inches.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

The heights of the men age 18 and over in HANES5 averaged 69 inches; the SD was 3 inches.

This means that \mu = 69, \sigma = 3

Such a man that is 6 feet tall is at the percentile of this height distribution.

6 feet = 6*12 inches = 72 inches. So this percentile is the p-value of Z when X = 72. So

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

Z = \frac{72 - 69}{3}

Z = 1

Z = 1 has a p-value of 0.84, so 84th percentile.

What is the 25th percentile, to the nearest inch

X when Z has a p-value of 0.25, so X when Z = -0.675.

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

-0.675 = \frac{X - 69}{3}

X - 69 = -0.675*3

X = 67

The 25th percentile is of 67 inches.

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3 years ago
13/19x=130 how do I solve?
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Divide both numbers by 13/90

13/90x = 130
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A. 4.25p + 3.79c

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2 years ago
Zander read 13 3/4pages in 1/4 of an hour. Sydney read 43 1/3 pages in 2/3 of an hour. At these rates, would Zander or Sydney re
kakasveta [241]

Answer:

At these rates Sydney read 10 pages per hour more than Zander.

Step-by-step explanation:

Zander read 13\frac{3}{4} pages in \frac{1}{4} of an hour.

Therefore, pages read by Zander in 1 hour = \frac{\text{Total pages read}}{\text{Total time taken}}

= \frac{13\frac{3}{4}}{\frac{1}{4}}

= \frac{55}{4}\times \frac{4}{1}

= 55 pages per hour

Sydney read 43\frac{1}{3} pages in \frac{2}{3} of an hours.

Pages read by Sydney in 1 hour = \frac{43\frac{1}{3}}{\frac{2}{3} }

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= 65 pages per hour

Therefore, number of pages read more by Sydney as compared to Zander,

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At these rates Sydney read 10 pages per hour more than Zander.

4 0
2 years ago
Suppose f(x)=2×+5 find the value of -2f(x+1)
loris [4]
F(x) = 2x + 5 

-----------------------------------
Find f(x + 1) :
-----------------------------------
f(x +1) = 2(x + 1) + 5
f(x +1) = 2x + 2 + 5
f(x + 1) = 2x + 5

-----------------------------------
Find -2f(x+1):
-----------------------------------
-2(fx+1) = -2(2x + 5)
-2(fx+1) = -4x - 10

----------------------------------------------------------------------
Answer: -2(fx+1) = -4x - 10
----------------------------------------------------------------------
3 0
3 years ago
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