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marissa [1.9K]
3 years ago
15

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

speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.
The value to use for the standard error of the mean is:

1.13.5
2.9
3.2.26
4.1.5
Mathematics
1 answer:
myrzilka [38]3 years ago
7 0

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

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5x+9=2x+7+3x-15
andrew11 [14]

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Step-by-step explanation:

Step 1:

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Step 2:

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Hope This Helps :)

3 0
3 years ago
Read 2 more answers
Last question please
MatroZZZ [7]

Let's try an make a formula to make things easy.

_________________________________________________

Look at Andrew's pattern, it goes up 6 every time. Lets look at the 6 times table

6 times table:           6, 12, 18, 24, ...

____________________________________

First think, how would you work out the <u>7</u>th term in the <u>6</u>th times table?

You would do <u>6</u> times <u>7</u>.

So the formula for the 6th times table is:

6n     (where n is the term you want to find out)

_______________________________________

So to get the 9th term in the 6 times table, you would replace the n with 9, like so:

9th term in 6 times table = 6 x 9 = 54

______________________________________

Now lets compare the 6 times table to Andrew's pattern:

6 times table:           6, 12, 18, 24,

Andrew's pattern:     3, 9, 15, 21,

_____________________________________

If you look, you can see that Andrew's pattern is the 6 times table minus 3!

So what would be the formula for Andrew pattern?

---> it would be:  6n - 3   (since it's the 6 times table but minus 3)

_____________________________________

We can use this formula to easily work out the 20th term in Andrew's pattern!:

20th term = 6 x 20 - 3 = 120 - 3 = <u>117</u>    (remember, replace the n with 20)

______________________________________

Now let's make a formula for Ben's pattern!

Ben's pattern goes up in 5s, so lets compare it to the 5 times table:

5 times table:       5, 10, 15, 20

Ben's pattern:       3, 8, 13, 18,

The formula for the 5 times table is 5n, and Ben's pattern is the 5 times table but minus 2.

So the formula for Ben's pattern is: 5n - 2

__________________________________

<u>Now swap out the n for 20</u>  (to get the 20th term):

20th term = 5 x 20 - 2 = 100 - 2 = <u>98</u>

_________________________________________

So Andrew's 20th term is <u>117</u>, and Ben's 20th term is <u>98</u>.

All we do now is subtract them to find the difference:

117 - 98 = <u>19</u>

- - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

Ben's 20th term is smaller by 19!

- - - - - - - - - - - - - - - - - - - - - - - - - -

5 0
3 years ago
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