Answer:
a.) Minimum test score = 41
Maximum test score = 95
b.)An approximate value of the standard deviation is 9.
Step-by-step explanation:
The given set of test scores is approximately bell shaped.
The mean of the test scores,
= 68
The range of the data set = 54.
a.) i.) Minimum test score = ![\mu - \frac{range}{2} = 68 - \frac{54}{2} = 68 - 27 = 41](https://tex.z-dn.net/?f=%5Cmu%20-%20%5Cfrac%7Brange%7D%7B2%7D%20%20%3D%2068%20-%20%5Cfrac%7B54%7D%7B2%7D%20%20%3D%2068%20-%2027%20%3D%2041)
ii.) The maximum test score = ![\mu + \frac{range}{2} = 68 + \frac{54}{2} = 68 + 27 = 95](https://tex.z-dn.net/?f=%5Cmu%20%2B%20%5Cfrac%7Brange%7D%7B2%7D%20%20%3D%2068%20%2B%20%5Cfrac%7B54%7D%7B2%7D%20%20%3D%2068%20%2B%2027%20%3D%2095)
b.) From the 68-95-99.7 rule, also known as the Empirical rule, tell us that an approximation of the range is 3 standard deviations either way from the mean. So from this rule we can say that the minimum can also be found from
and the maximum can also be approximated as
.
From the above we can say that the range can be written as
![3\sigma - (-3\sigma) = range](https://tex.z-dn.net/?f=3%5Csigma%20-%20%28-3%5Csigma%29%20%3D%20range)
∴ ![6\sigma = range](https://tex.z-dn.net/?f=6%5Csigma%20%20%3D%20range)
∴ ![\sigma = \frac{range }{6} = \frac{54}{6} = 9](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%5Cfrac%7Brange%20%7D%7B6%7D%20%20%3D%20%5Cfrac%7B54%7D%7B6%7D%20%20%3D%209)
Therefore an approximate value of the standard deviation is 9.
Answer:
D. Jake and Liu
Step-by-step explanation:
41 is prime so Teresa is wrong. The other two are not prime.
Perimeter is 24.
Length is 4 greater than the width.
Let's use 'x' for width
we can write this as x+4 + x+4 + x + x
x+4 being the width+4 and x being the width
There are 4 sides to a rectangle so you are adding 4 values
Two length and two widths
so we can then combine the two lengths to make 2x+8
and then combine the two widths to make 2x
Then put it together. 2x+2x+8= 4x+8
4x+8=24
Subtract 8 from both sides
4x=16
divide both sides by 4
x=4
The width is 4.
Answer:
Math
Step-by-step explanation:
I dont know sorry I'm not good at math.
Answer:
4
Step-by-step explanation:
We can start by seeing the difference between -4 and -8. They have a difference of 4, so the middle number is 2 because 4/2 = 2. So now we can start skip counting, there are 4 lines between -4 and the blue dot. So 4*2 = 8. -4+8=4. So our answer is 4.