Which set of ordered pairs represents a function?

A simple random sample of size nequals=8181 is obtained from a population with mu equals 77μ=77 and sigma equals 27σ=27. (a) De

ivanzaharov [21]

Answer:

a) $P(\bar X>81.5)=1-0.933=0.067$

b) $P(\bar X$

c) $P(73.4$

Step-by-step explanation:

1) 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".

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

$X \sim N(\mu=77,\sigma=27)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

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

On this case $\bar X \sim N(77,\frac{27}{\sqrt{81}})$

Part a

We want this probability:

$P(\bar X>81.5)=1-P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X >81.5)=1-P(Z$

$P(\bar X>81.5)=1-0.933=0.067$

Part b

We want this probability:

$P(\bar X\leq 69.5)$

If we apply the formula for the z score to our probability we got this:

$P(\bar X \leq 69.5)=P(Z\leq \frac{69.5-77}{\frac{27}{\sqrt{81}}})=P(Z$

$P(\bar X\leq 69.5)=0.0062$

Part c

We are interested on this probability

$P(73.4$

If we apply the Z score formula to our probability we got this:

$P(73.4$

$=P(\frac{73.4-77}{\frac{27}{\sqrt{81}}}$

And we can find this probability on this way:

$P(-1.2$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1.2$

3 0

4 years ago

What is x cube + x square

MatroZZZ [7]

The answer is
x^5
is correct......

7 0

4 years ago

Choose the symbol that compares the fractions<br><br> 4/3 and 7/6<br><br> <,>,=

gulaghasi [49]

In order to compare them they need to have the same denominator. Which is 6

Multiply 4/3 by 2/2. You get 8/6

8/6>7/6

4/3>7/6

4 0

3 years ago

Read 2 more answers

What's the order 5/6 7/12 1/8 5/16

cluponka [151]

To find the order smallest to largest we need to find the common denominator the find the equivalent fractions and compare.

the LCD is 48 so

5/6 = 40/48
7/12 = 28/48
1/8 = 6/48
5/16 = 15/48

now we can make a direct comparison...
from smallest to largest
1/8, 5/16, 7/12, 5/6

7 0

3 years ago

Hunter wants to prove to his parents that playing computer games while he studies for tests will help him get better grades. He

mars1129 [50]

His mistake was that he did not use a random sample. His tried to show that playing games would give him higher grades which his study does not decisively conclude because the people around him that play games are likely to be in the same academic caste as him, which skews his data. Choice B would be the best because he's not testing any variables, rather just collecting the unadultered data of the group.

7 0

3 years ago