Answer:
a) 6.68th percentile
b) 617.5 points
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 problem, we have that:
![\mu = 550, \sigma = 100](https://tex.z-dn.net/?f=%5Cmu%20%3D%20550%2C%20%5Csigma%20%3D%20100)
a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.
![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{400 - 550}{100}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B400%20-%20550%7D%7B100%7D)
![Z = -1.5](https://tex.z-dn.net/?f=Z%20%3D%20-1.5)
has a pvalue of 0.0668
So this student is in the 6.68th percentile.
b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.
He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![0.675 = \frac{X - 550}{100}](https://tex.z-dn.net/?f=0.675%20%3D%20%5Cfrac%7BX%20-%20550%7D%7B100%7D)
![X - 550 = 0.675*100](https://tex.z-dn.net/?f=X%20-%20550%20%3D%200.675%2A100)
![X = 617.5](https://tex.z-dn.net/?f=X%20%3D%20617.5)
Alright my friend so basically if we subtract 5 from 71 we get 66 plus 8 would be 74 so we would have to drop the temp 3 degrees to get back to 71 so the answer will be option B. fall 3 degrees
Answer:
40 + 38w ≥ 265.49
Where “w” represents the amount
of weeks it will take to
save the money