A cone has volume 3. If the cone’s radius is 1, what is its height?

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

3 years ago

A 6-letter "word" is obtained by spinning a fair spinner (labeled a, b, and c) six times .

dimaraw [331]

Asked and answered elsewhere.
brainly.com/question/10294535

a) 10/81

b) 19/243

8 0

3 years ago

A random sample of 10 subjects have weights with a standard deviation of 11.0482 kg. What is the variance of their weights? Be

Paladinen [302]

Answer:

The variance is 122.0627 kg

Step-by-step explanation:

The square of the standard deviation of a distribution gives us the variance.

If a random sample of 10 subjects have weights with a standard deviation of 11.0482 kg.

Then the standard deviation is

${ \sigma} = 11.0482$

To get the variance, we square both sides to get;

${ \sigma}^{2} = 11.0482^{2}$

This implies that,

${ \sigma}^{2} = 122.0627kg$

7 0

3 years ago

Find the area of the following shape. You must show all work to receive credit.

statuscvo [17]

Answer:

8 unit ^2 or 8cm^2

Step-by-step explanation:

area 1

1/2 ( 3 x 3 ) = 4.5 unit ^2

area 2 we split the triangle into half

= 1/2 ( 2 x 2) = 2 unit ^2

we know the other half is also 2 unit ^2 but we add then subtract

1/2 (1 x 1) = 0.5^2

To get

4.5 + 2+ 2 - ( 0.5) = 8 unit ^2

8 0

3 years ago

What are the factors of x2 + 3x – 4?

lbvjy [14]

I get a list of zeroes: x = ±1, –3, 2 ... For instance, for x = 2 to be a solution, then I must have solved the factor equation x – 2 = 0, which means that x – 2 must have been a ... Find the quadratic with zeroes at x = 3/2 and x = –5/4

7 0

3 years ago

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