Mathematics, 01.11.2019 01:31 juansoto227711

Heights of men have a bell-shaped distribution, with a mean of 176 cm and a standard deviation of 7 cm. using the empirical rule, answer the following questions: a) what is the approximate percentage of men between 169 and 183 cm? b) between which 2 heights would 95% of men fall? c) is it unusual for a man to be more than 197 cm tall? explain.

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Answer from: lizzynmk

a) 68% of the men fall between 169 cm and 183 cm of height.

b) 95% of the men will fall between 162 cm and 190 cm.

c) It is unusual for a man to be more than 197 cm tall.

Step-by-step explanation:

The 68-95-99.5 empirical rule can be used to solve this problem.

This values correspond to the percentage of data that falls within in a band around the mean with two, four and six standard deviations of width.

a) What is the approximate percentage of men between 169 and 183 cm?

To calculate this in an empirical way, we compare the values of this interval with the mean and the standard deviation and can be seen that this interval is one-standard deviation around the mean:

$\mu-\sigma=176-7=169\\\mu+\sigma=176+7=183$

Empirically, for bell-shaped distributions and approximately normal, it can be said that 68% of the men fall between 169 cm and 183 cm of height.

b) Between which 2 heights would 95% of men fall?

This corresponds to ±2 standard deviations off the mean.

$\mu-2\sigma=176-2*7=162\\\\\mu+2\sigma=176+2*7=190$

95% of the men will fall between 162 cm and 190 cm.

c) Is it unusual for a man to be more than 197 cm tall?

The number of standard deviations of distance from the mean is

n=(197-176)/7=3

The percentage that lies outside 3 sigmas is 0.5%, so only 0.25% is expected to be 197 cm.

It can be said that is unusual for a man to be more than 197 cm tall.

Answer from: Quest

yes because they have the same amount of green and blur marbles.

step-by-step explanation:

Answer from: Quest

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

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Heights of men have a bell-shaped distribution, with a mean of 176 cm and a standard deviation of 7...

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