Question

A certain math test has a mean of 50 and a standard deviation of 12. the teacher wants to convert the scores to a new scale using the transformation x*=65+0.6x. what are the new mean and standard deviation?

a) mean=50, standard deviation=7.2
b) mean=95, standard deviation=7.2
c) mean=95, standard deviation=12
d) mean=95, standard deviation=72.2
e) mean=77, standard deviation=12

Answer 1

(b) mean=95, standard deviation=7.2.

Explanation:

To find the new mean and standard deviation, we first need to apply the transformation to the original mean and standard deviation.

The new mean is given by: x*=65+0.6x

Substituting in the original mean of 50, we get: x*=65+0.6(50) = 95

The new standard deviation is given by: s*=0.6s

Substituting in the original standard deviation of 12, we get: s*=0.6(12) = 7.2

Therefore, the new mean and standard deviation are (b) mean=95, standard deviation=7.2.