Answer:
a) Grade = 93, Standard score = 1.5
Grade = 62, Standard score = -1.6
b) Standard scores = 0.6, Grade = 84
Standard scores = 1.2, Grade = 90
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 78
Standard Deviation, σ = 10
Formula:
![z_{score} = \displaystyle\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z_%7Bscore%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
a) Grade = 93
![\text{Standard score } = \displaystyle\frac{93-78}{10} = 1.5](https://tex.z-dn.net/?f=%5Ctext%7BStandard%20score%20%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B93-78%7D%7B10%7D%20%3D%201.5)
Grade = 62
![\text{Standard score } = \displaystyle\frac{62-78}{10} = -1.6](https://tex.z-dn.net/?f=%5Ctext%7BStandard%20score%20%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B62-78%7D%7B10%7D%20%3D%20-1.6)
b) We have to find grades of student
Standard scores = 0.6
![\displaystyle\frac{x-78}{10} = 0.6\\\\x = (0.6)(10)+78 \\x = 84](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bx-78%7D%7B10%7D%20%3D%200.6%5C%5C%5C%5Cx%20%3D%20%280.6%29%2810%29%2B78%20%5C%5Cx%20%3D%2084)
Grade = 84
Standard scores = 1.2
![\displaystyle\frac{x-78}{10} = 1.2\\\\x = (1.2)(10)+78 \\x = 90](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bx-78%7D%7B10%7D%20%3D%201.2%5C%5C%5C%5Cx%20%3D%20%281.2%29%2810%29%2B78%20%5C%5Cx%20%3D%2090)
Grade = 90
Answer:
the outlier is 20 and 24
Step-by-step explanation: An outlier, in mathematics, statistics and information technology, is a specific data point that falls outside the range of probability for a data set. In this Case 20 and 24 are outliers because they are not in the range of 58, 59, 63, 63, 65, 66. :) your welcome.
Well, the first 16 were about 16*75=$1200 extra. The last 8 were $720 lost. Thus, the total profit is $480. He bought them with $7200, which means the profit is around 6.67%.