81 as a mixed number simplified

A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of

myrzilka [38]

Answer:

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(60,13.5)$

Where $\mu=60$ and $\sigma=13.5$

And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error of the mean would be:

$\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5$

4.1.5

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(60,13.5)$

Where $\mu=60$ and $\sigma=13.5$

And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error of the mean would be:

$\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5$

4.1.5

7 0

4 years ago

Water boils at 100LaTeX: ^\circ∘ Celsius or 212LaTeX: ^\circ∘ Fahrenheit. Water freezes at 0LaTeX: ^\circ∘ Celsius or 32LaTeX: ^

Lubov Fominskaja [6]

Answer:

$F = 1.8C +32$

$F = 86^{\circ}F$

Step-by-step explanation:

Represent Celsius with C and Fahrenheit with F.

So, we have:

$(C_1,F_1) = (100,212)$

$(C_2,F_2) = (0,32)$

Solving (a): Represent as a linear equation

First, we calculate the slope:

$m = \frac{F_2 - F_1}{C_2 - C_1}$

This gives:

$m = \frac{32 - 212}{0 - 100}$

$m = \frac{-180}{- 100}$

$m = 1.8$

The linear equation is then calculated using:

$F - F_1 = m(C -C_1)$

Where

$(C_1,F_1) = (100,212)$

$m = 1.8$

$F - 212 = 1.8(C -100)$

$F - 212 = 1.8C -180$

Make F the subject

$F = 1.8C -180+212$

$F = 1.8C +32$

Solving (b): The value of F when C = 30

Substitute 30 for C in $F = 1.8C +32$

$F = 1.8 * 30 + 32$

$F = 54 + 32$

$F = 86$

8 0

3 years ago

Read 2 more answers

What is the quotient of 78.3 ÷ 3.48?

olga_2 [115]

The answer is 22.5. I hope this helps you.

Good luck with your work!

8 0

3 years ago

Herman saves 22% of his monthly paycheck so he can buy a new car. He earned $825 last month. How much money did Herman save for

djyliett [7]

Answer:$181.5

Step-by-step explanation:

8 0

3 years ago

Write the unit rate and the rate 15 points scored in 4 quarters

Trava [24]

You first divide both numbers by 4 to get one quarter which is the unit, and to get the rate, you divide 15 by 4 also. i got the unit rate is 3.75 points oer quarter.

3 0

4 years ago