A distribution of 200 scores has a standard deviation of 10

A distribution of 200 scores has a standard deviation of 10. A constant of 25 is added to each score in the distribution. The transformed distribution has a variance of ___________

Use the z distribution table to answer the following question: What portion of the standard normal distribution falls between the mean and a z score of 1.0. (Note you are ask for the portion.)

Use the z distribution table to answer the following question: Most personality tests have a mean of 50 and a standard deviation of 10. Given that a measure of depression is normally distributed with a mean of 50 and a SD of 10, what percentage of individuals will have scores on the depression test above 65? (Note that typically the higher the score on the personality measure then the \"worse\" the symptoms. So a score of 65 might be used as a cutoff for identifying individuals who might be classified as having clinical depression.) (Remember to answer with a percent and not a portion.)

Solution

The variance remains the same when a constant is added.

P( -z < Z < z) = 0.1

P( Z< z) - P( Z < -z) = 0.1

2P( Z < z) - 1 = 0.1

P( Z < z) = 0.55

Z = 0.125

X : Depression test scores

X ~ N(50 , 100)

P( X > 65)

= P( Z > (65 - 50)/10)

= P( Z > 1.5)

= 0.0668

6.68% of the individuals will have scores on the depression test above 65.