The population mean on a statistics exam is 72, with a standard deviation of 12. The population average on the class project is 95, with a standard deviation of 4. If the exam is 70% of the final grade and the project 30%, what are the mean and standard deviation of final grades?

mean = 54

standard deviation = 6.24

Explanation:

given data

mean a = 72

standard deviation σx = 12

average b = 95

standard deviation σy = 4

final grade Z = 70% = 0.70

project y = 30% = 0.30

to find out

mean and standard deviation

solution

final grade equation will be here

final grade = 0.70x + 0.30 y ... a

here x is statics grade and y is class project

so

mean will be 0.70x + 0.30 y

mean = 0.70 (a) + 0.30 (b)

mean = 0.70 (12) + 0.30 (95)

mean = 54

and

standard deviation = 0.70x + 0.30 y

standard deviation = 0.70 (σx) + 0.30 (σy)

standard deviation = 0.70 (12) + 0.30 (4)

standard deviation = 6.24