-9m+81-m^2+9m = 81 - m^2 (final answer since -9m and 9m cancels each other out)
Answer:
Step-by-step explanation:
Hello!
The variable of interest is the readings on thermometers. This variable is normally distributed with mean μ= 0 degrees C and standard deviation σ= 1.00 degrees C.
The objective is to find the readings that are in the top 3.3% of the distribution and the lowest 3.3% of the distribution.
Symbolically:
The lower value P(X≤a)=0.033
Top value P(X≥b)=0.033
(see attachment)
Lower value:
The accumulated probability until "a" is 0.03, since the variable has a normal distribution, to reach the value of temperature that has the lowest 3.3%, you have to work under the standard normal distribution.
First we look the Z value corresponding to 0.033 of probability:
Z= -1.838
Now you reverste the standardization using the formula Z= (a-μ)/δ
a= (Z*δ)+μ
a= (-1.838*1)+0
a= -1.838
Top value:
P(X≥b)=0.033
This value has 0.033 of the distribution above it then 1 - 0.033= 0.967
is below it.
You can rewrite the expression as:
P(X≤b)=0.967
Now you have to look the value of Z that corresponds to 0.967 of accumulated probability:
b= (Z*δ)+μ
b= (1.838*1)+0
b= 1.838
The cutoff values that separates rejected thermometers from the others are -1.838 and 1.838 degrees C.
I hope it helps!
Answer:
-0.462
Step-by-step explanation:
The null hypothesis is:
![H_{0} = 0.25](https://tex.z-dn.net/?f=H_%7B0%7D%20%3D%200.25)
The alternate hypotesis is:
![H_{1} \neq 0.25](https://tex.z-dn.net/?f=H_%7B1%7D%20%5Cneq%200.25)
Our test statistic is:
![t = \frac{X - \mu}{s}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7Bs%7D)
In which X is the sample mean,
is the population mean(the null hypothesis),
is s is the standard deviation of the sample.
In this problem:
![X = \frac{23}{100} = 0.23, \mu = \frac{25}{100} = 0.25, s = \sqrt{\frac{0.25*0.75}{100}} = 0.0433](https://tex.z-dn.net/?f=X%20%3D%20%5Cfrac%7B23%7D%7B100%7D%20%3D%200.23%2C%20%5Cmu%20%3D%20%5Cfrac%7B25%7D%7B100%7D%20%3D%200.25%2C%20s%20%3D%20%5Csqrt%7B%5Cfrac%7B0.25%2A0.75%7D%7B100%7D%7D%20%3D%200.0433)
So
![t = \frac{0.23 - 0.25}{0.0433} = -0.462](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B0.23%20-%200.25%7D%7B0.0433%7D%20%3D%20-0.462)
So the correct answer is:
-0.462
Answer:
2.5 km left
The midpoint is half of 5, which is 2.5, so he'll still have 2.5 km left to complete
Answer:
39°
Step-by-step explanation:
IM assuming xyz is a triangle
180 - 113 - 28 = 67 - 28 = 39