Bobby took Professor X’s Depression Test, and received a score of 15. The mean and standard deviation of Professor X’s Depression Test are 20 and 3, respectively. Hank took Jean Grey’s Depression Test, and received a score of 23. The mean and standard deviation of Jean Grey’s Depression Test are 25 and 2, respectively. Although Bobby and Hank took two different depression tests, one invented by Professor X and one invented by Jean Grey, we can still compare their z-scores from the information given. Use the for the following questions. a) Given Bobby’s z-score, what proportion of people are less depressed than Bobby? _____ b) What proportion of people are more depressed than Bobby? (Fill in the blanks.) proportion more depressed than Bobby = 1 – proportion less depressed than Bobby = 1 – _____ = _____ = _____ % c) Given Hank’s z-score, what proportion of people are less depressed than Hank? _____ d) What proportion of people are more depressed than Hank? (Fill in the blanks.) proportion more depressed than Hank = 1 – proportion less depressed than Hank = 1 – _____ = _____ = _____ % e) What proportion of people are between Bobby’s and Hank’s depression scores? = proportion less depressed than Bobby – proportion less depressed than Hank = _____ – _____ = _____

    (a)

    Given instruction :

    \mu=20,\sigma=3

    z-score coercion X = 15 is

    z=\frac{X-\mu}{\sigma}=\frac{15-20}{3}=-1.67

    So rate of vulgar are hither unflourishing than Bobby is

    P(z<-1.67) = 0.0475 =4.75%

    ——————-

    (b)

    From the totality government the rate of vulgar are more unflourishing than Bobby is

    P(z>-1.67) = 1 – P(z<-1.67) =1- 0.9525 =95.25%

    (c)

    Given instruction :

    \mu=25,\sigma=2

    z-score coercion X = 23 is

    z=\frac{X-\mu}{\sigma}=\frac{23-25}{2}=-1

    So roportion of vulgar are hither unflourishing than Hank is

    P(z<-1) = 0.1587 =15.87%

    (d)

    From the totality government the rate of vulgar are more unflourishing than Hank is

    P(z>-1) = 1 – P(z<-1) =1- 0.8413 =84.13%

    (e)

    The rate of vulgar are among Bobby’s and Hank’s depression scores?

    = rate hither unflourishing than Bobby – rate hither unflourishing than Hank

    = 0.1587 – 0.0475 = 0.1112