Answer:
3/4
Step-by-step explanation:
I think
Hope this helps
Answer:
a) ![\bar X \sim N(40,\frac{5}{\sqrt{64}}=0.625)](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Csim%20N%2840%2C%5Cfrac%7B5%7D%7B%5Csqrt%7B64%7D%7D%3D0.625%29)
b) ![P(39.6 \leq \bar X \leq 40.4)=0.4778](https://tex.z-dn.net/?f=P%2839.6%20%5Cleq%20%5Cbar%20X%20%5Cleq%2040.4%29%3D0.4778)
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".
Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:
And let
represent the sample mean, the distribution for the sample mean is given by:
(a) What are the mean and standard deviation of the sampling distribution?
![\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Csim%20N%28%5Cmu%2C%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%29)
On this case ![\bar X \sim N(40,\frac{5}{\sqrt{64}}=0.625)](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Csim%20N%2840%2C%5Cfrac%7B5%7D%7B%5Csqrt%7B64%7D%7D%3D0.625%29)
(b) What is the approximate probability that x will be within 0.4 of the population mean μ? (Round your answer to four decimal places.) P =
So for this case we want this probability:
![P(40-0.4 \leq \bar X \leq 40+0.4)= P(39.6 \leq \bar X \leq 40.4)](https://tex.z-dn.net/?f=P%2840-0.4%20%5Cleq%20%5Cbar%20X%20%5Cleq%2040%2B0.4%29%3D%20P%2839.6%20%5Cleq%20%5Cbar%20X%20%5Cleq%2040.4%29)
And for this case we can use the z score given by this formula:
![Z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
And using this concept we got this:
![P(\frac{39.6 -40}{\frac{5}{\sqrt{64}}} \leq \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}} \leq \frac{40.4 -40}{\frac{5}{\sqrt{64}}})](https://tex.z-dn.net/?f=P%28%5Cfrac%7B39.6%20-40%7D%7B%5Cfrac%7B5%7D%7B%5Csqrt%7B64%7D%7D%7D%20%5Cleq%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%20%5Cleq%20%5Cfrac%7B40.4%20-40%7D%7B%5Cfrac%7B5%7D%7B%5Csqrt%7B64%7D%7D%7D%29)
![P(-0.64 \leq Z \leq 0.64) =P(z](https://tex.z-dn.net/?f=P%28-0.64%20%5Cleq%20Z%20%5Cleq%200.64%29%20%3DP%28z%3C0.64%29-P%28Z%3C-0.64%29%3D0.7389-0.2611%3D0.4778)
Answer:
-75 0 25 50
Step-by-step explanation:
Answer:
The answer is B.
Step-by-step explanation:
You have to substitute x = 2, into the equation of y :
![y = 6 {x}^{3} - 5 {x}^{2} + 4x - 3](https://tex.z-dn.net/?f=y%20%3D%206%20%7Bx%7D%5E%7B3%7D%20%20-%205%20%7Bx%7D%5E%7B2%7D%20%20%2B%204x%20-%203)
![let \: x = 2](https://tex.z-dn.net/?f=let%20%5C%3A%20x%20%3D%202)
![y = 6 {( 2)}^{3} - 5 {(2)}^{2} + 4(2) - 3](https://tex.z-dn.net/?f=y%20%3D%206%20%7B%28%202%29%7D%5E%7B3%7D%20%20-%205%20%7B%282%29%7D%5E%7B2%7D%20%20%2B%204%282%29%20-%203)
![y = 48 - 20 + 8 - 3](https://tex.z-dn.net/?f=y%20%3D%2048%20-%2020%20%2B%208%20-%203)
![y = 33](https://tex.z-dn.net/?f=y%20%3D%2033)
Answer:
zero, or 0, or none. answer is A
Step-by-step explanation:
they never touch, just pick A