How many 4-digit multiples of 2 are there?

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.69 inches

Brilliant_brown [7]

Answer:

a) 1.93

b) 97.32% of men are SHORTER than 6 feet 3 inches

c) 2.71

d) 0.34% of women are TALLER than 5 feet 11 inches

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.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

For man, $\mu = 69.8, \sigma = 2.69$

A feet has 12 inches, so this is Z when X = 6*12 + 3 = 75. So

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

$Z = \frac{75 - 69.8}{2.69}$

$Z = 1.93$

b. What percentage of men are SHORTER than 6 feet 3 inches?

Z = 1.93 has a pvalue of 0.9732

97.32% of men are SHORTER than 6 feet 3 inches

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

For woman, $\mu = 64.1, \sigma = 2.55$

Here we have X = 5*12 + 11 = 71.

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

$Z = \frac{71 - 64.1}{2.55}$

$Z = 2.71$

d. What percentage of women are TALLER than 5 feet 11 inches?

Z = 2.71 has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.34% of women are TALLER than 5 feet 11 inches

5 0

4 years ago

Your towns public library is building a new wheelchair ramp to its entrance. By law the maximum angle of incline for the ramp is

Mrrafil [7]

For this case we can model the problem as a rectangle triangle.
We have the angle between the base and the hypotenuse of the triangle.
We have the height of the triangle.
We want to calculate the base of the triangle.
For this, we use the following trigonometric relationship:
$tan (4.76) = 2 / x
$
Clearing x we have:
$x = 2 / tan (4.76)

 x = 24.02 feet$
Answer:
the shortest horizontal distance that the ramp can span is:
x = 24.02 feet

6 0

3 years ago

Read 2 more answers

A basketball team wants to paint half of a free-throw circle grey. If the circumference of the free-throw circle is 30.77 feet,

Nezavi [6.7K]

Answer:

37.7 ft²

Step-by-step explanation:

2×3.14×r=30.77

<em>Divide both sides by 2</em>

3.14×r=15.385

<em>Divide both sides by 3.14</em>

r≈4.9

3.14×r²

3.14×4.9²=

24.01×3.14≈

75.4

75.4÷2=

37.7

6 0

4 years ago

two bags and four hats cost $100 in all. three bags and seven hats cost $164 in all. what is the cost of 1 hat?

Natali [406]

Answer:

Bags = 22

Hat = 14

22 x 2 = 44

14 x 4 = 56

So the first part is true

3 x 22 = 66

7 x 14 = 98

So the second part is true

14 is the answer

It's trial and error

Step-by-step explanation:

4 0

4 years ago

1/15x = 10 solve x pls help its for a test

Travka [436]

Answer:

X=0.00667

Step-by-step explanation:

1/15x=10

multiply 15x the two sides

=15X*1/15x=15X*10

=drop 15x the left side

1=150X

=150X/150=1/150

therefore X=0.00667

7 0

3 years ago