Question

The scores from the first test for students in my statistics class have an average of 70 and a standard deviation of 3. The scores from the second test has the same average and standard deviation as scores from the first test. The variance of the score from the second test given that the score in the first test is 65, is 2. Assume the scores of the students in the first test and second test are positively correlated and have a bivariate normal distribution. Calculate the average scores of the students in the second test given that the scores in the first test are 65.

Answer 1

`P(Y| X = 65)=66`

Explanation:

From the question we are told that:

Mean
`\=x=70`

Standard Deviation
`\sigma=3`

Variance
`\sigma^2=2`

Generally the equation for Variance of Prediction is mathematically given by

`\sigma_(p)^2=\sigma_(p)'^2*(1-r^2)`

Where

`\sigma_(p)'^2=variance\ of\ predictor`

Therefore

`2=3^2*(1-r^2)\\\\r=0.88`

Therefore

The Average score of student in 2nd test

`P(Y| X = x) = \mu +(p\sigma)/(\sigma(x −\mu_X))`

`P(Y| X = 65) = 70 +0.88(3)/(3))*(65-70)`

`P(Y| X = 65)=66`