(3.20) According to a study, the scale of scores on an IQ test of adults is appr

Question

(3.20) According to a study, the scale of scores on an IQ test of adults is approximately Normal with mean 100 and standard deviation 16. The organization MENSA, which calls itself "the high-IQ society," requires an IQ score of 130 or higher for membership.

What percent of adults (± 0.1%) would qualify for membership?    %

Start by calculating a z-score for the IQ needed to qualify. What percent of people will have IQs at least this high?

(3.22) The proportion of observations from a standard Normal distribution that take values greater than 1.321.32 is about (±± 0.001)

(3.22) The proportion of observations from a standard Normal distribution that take values less than -1.39 is about (±± 0.0001)

(3.20) According to a study, the scale of scores on an IQ test of adults is approximately Normal with mean 100 and standard deviation 16. The organization MENSA, which calls itself "the high-IQ society," requires an IQ score of 130 or higher for membership.

What percent of adults (± 0.1%) would qualify for membership?    %

Start by calculating a z-score for the IQ needed to qualify. What percent of people will have IQs at least this high?

Explanation / Answer

3.20) Mean = 100

Standard deviation = 16

P(X < A) = P(Z < (A - mean)/standard deviation)

P(X>130) = 1 - P(X < 130)

= 1 - P(Z < (130 - 100)/16)

= 1 - P(Z < 1.875)

= 1 - 0.9696

= 0.0304

=3.04%

14)P(Z > 1.32) = 1 - P(Z < 1.32)

= 1 - 0.9066

= 0.0934

15) P(Z < -1.39) = 0.0823

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.