Answer:
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
Step-by-step explanation:
When the distribution is normal, we use 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, we have that:
![\mu = 22, \sigma = 5.1](https://tex.z-dn.net/?f=%5Cmu%20%3D%2022%2C%20%5Csigma%20%3D%205.1)
Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?
The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.
![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{24 - 22}{5.1}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B24%20-%2022%7D%7B5.1%7D)
![Z = 0.39](https://tex.z-dn.net/?f=Z%20%3D%200.39)
has a pvalue of 0.6517
1 - 0.6517 = 0.3483
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
-4x + 4 = 6
x = -.5
2x + 10 = 50
x = 20
-3x - 14 = -5
x = -3
2/3x + 2 = 5
x = 4.5
Answer:
b=12-4a
a+b=28
Step-by-step explanation:
solve using a system of equations method. hope this helps! :)
Divide the amount of AU$ by the equivalent to 1 US$ (1USD=1.2AU)
So, 22 divided by 1.2 = 18.33