Question-43

If the mean and standard deviation of observations \(x_1, x_2, \ldots, x_n\) are 20 and 5 respectively, and the mean and standard deviation of observations \(a(3x_1+b), a(3x_2+b), \ldots, a(3x_n+b)\) are 94.5 and 22.5 respectively, then what is the sum of \(a\) and \(b?\) Enter the answer correct to one decimal place.

Hint

Use the property of “Effect on mean and variance when constants are added or multiplied.

Answer

4.5

Solution