Question

5. A population with mean = 37 and standard deviation = 6 is standardized so that the new mean is 50 and the new standard deviation is 10. A scale of 40 on the first scale is equivalent to what score on the new standardized scale?

Answer 1

Using z-scores, it is found that a scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.

What are z-scores?

The z-score of a measure X of a distribution with mean represented by $\mu$ and standard deviation represented by $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean.

• Looking at the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.

For the first scale, the parameters are given as follows:

$X = 40, \mu = 37, \sigma = 6$

Hence the z-score is:

$Z = \frac{X - \mu}{\sigma}$

Z = (40 - 37)/6

Z = 0.5.

For the second scale, we want to find X when Z = 0.5, considering the following mean and standard deviation:

$\mu = 50, \sigma = 10$

Hence:

$Z = \frac{X - \mu}{\sigma}$

0.5 = (X - 50)/10

X - 50 = 5

X = 55.

A scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.

More can be learned about z-scores at brainly.com/question/4079902

#SPJ1