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S.M.A.R.T. test scores are standardized to produce a normal distribution with a mean of 230 and...

  1. S.M.A.R.T. test scores are standardized to produce a normal distribution with a mean of 230 and a standard deviation of 35. Find the proportion of the population in each of the following S.M.A.R.T. categories. (6 points)
    1. Genius: Score of greater than 300.
    2. Superior intelligence: Score between 270 and 290.
    3. Average intelligence: Score between 200 and 260.
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Answer #1

Solution:

mean = 230

standard deviation of 35

a)

Genius: Score of greater than 300.

P(Genius)

= P(X > 330)

= P(z > (330 - 230)/35)

= P(z > 2.86)

= 0.0021

b) Superior intelligence: Score between 270 and 290

P(Superior intelligence)

= P(270< X < 290)

=  

= P(1.1428< z < 1.7142)

= 0.0835

c)

Average intelligence: Score between 200 and 260.

P(Average intelligence)

= P(200< X < 260)

=

= P(-0.8571< z < 0.8571)

=  0.6102

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