Answer:
0.1069 = 10.69%
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
![\mu = 45, \sigma = 10](https://tex.z-dn.net/?f=%5Cmu%20%3D%2045%2C%20%5Csigma%20%3D%2010)
Between 57 and 69
This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So
X = 69
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{69 - 45}{10}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B69%20-%2045%7D%7B10%7D)
![Z = 2.4](https://tex.z-dn.net/?f=Z%20%3D%202.4)
has a pvalue of 0.9918
X = 57
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{57 - 45}{10}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B57%20-%2045%7D%7B10%7D)
![Z = 1.2](https://tex.z-dn.net/?f=Z%20%3D%201.2)
has a pvalue of 0.8849
0.9918 - 0.8849 = 0.1069 = 10.69%
27^(4/3)+4^(3/2) can be simplified using roots.
The cube root of 27 is 3 and the square root of 4 is 2. This removes the denominators from the expression. The expression is now 3^4+2^3.
Simplify this and you get 81+8=89
Answer:
?????????
Step-by-step explanation:
What are u asking
Answer:
Well, 80 x 62.5% is 50.
So, 65 + 50 is 115.
I think there is a mistake in the question
Well, It could not, but please check again TT
Step-by-step explanation:
Answer:
x= 7
Step-by-step explanation:
11x-2 = 75
11(7) - 2
77 - 2 = 75
x= 7