Answer:
it's 86
Step-by-step explanation:
100-3x6+5-4
100-15+5-4
85+5-4
90-4
86
Answer: the night temperature was 3 degrees below the afternoon temperature
Step-by-step explanation:
All but kite, and the trapezoids
Answer:
The cutoff for an A grade is 82.8.
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 = 70, \sigma = 10](https://tex.z-dn.net/?f=%5Cmu%20%3D%2070%2C%20%5Csigma%20%3D%2010)
a. What is the cutoff for an A grade?
The top 10% of the class get an A grade. So the cutoff is the value of X when Z has a pvalue of 1-0.1 = 0.9. So it is X when Z = 1.28
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![1.28 = \frac{X - 70}{10}](https://tex.z-dn.net/?f=1.28%20%3D%20%5Cfrac%7BX%20-%2070%7D%7B10%7D)
![X - 70 = 1.28*10](https://tex.z-dn.net/?f=X%20-%2070%20%3D%201.28%2A10)
![X = 82.8](https://tex.z-dn.net/?f=X%20%3D%2082.8)
The cutoff for an A grade is 82.8.