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3 years ago

The product of two Even numbers

Mathematics

1 answer:

krek1111 [17]3 years ago

3 0

The product of two even numbers is even.

Let m and n be any integers so that 2m and 2k are two even numbers.

The product is 2m(2k) = 2(2mk), which is even.

Things to think about:

Why didn’t I just show you by using any two even numbers like the number 4 and the number 26?

Why did I change from "m" to "k" ? Are they really different numbers or could they be the same?

Why did I specifically say that m and k were integers?

The product of two odd numbers is an odd number.

Let m and k be any integers. This means that 2m+1 and 2k+1 are odd numbers.

The product is 4mk + 2m + 2k + 1 (hint: I used FOIL) which can be written as

2 ( 2mk + m + k ) + 1 which is an odd number.

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3 years ago

To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

nexus9112 [7]

Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

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

This Zscore is how many standard deviations the value of the measure X 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) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

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

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$