The scale of scores on an IQ test is approximately Normal with mean 101 and stan

Question

The scale of scores on an IQ test is approximately Normal with mean 101 and standard deviation 11. The organization MENSA, which calls itself "the high IQ society," requires an IQ score of 130 or higher for membership. Use this information to answer the following questions.

a) What proportion of adults would qualify for membership? (Use 4 decimal places.)

(b) Corinne scored 118 on her IQ test. Her z-score is about: (Use 2 decimal places.)

(c) Corinne scored 118 on her IQ test. She scored higher than what percent of all adults? (Use 2 decimal places.)

Explanation / Answer

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    130      
u = mean =    101      
          
s = standard deviation =    11      
          
Thus,          
          
z = (x - u) / s =    2.636363636      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.636363636   ) =    0.004189994 [ANSWER]

***************

b)

As z = (x - u) / s, then as          
          
x = critical value =    118      
u = mean =    101      
          
s = standard deviation =    11      
          
Thus,          
          
z = (x - u) / s =    1.545454545   [ANSWER]

****************  
          
c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    118      
u = mean =    101      
          
s = standard deviation =    11      
          
Thus,          
          
z = (x - u) / s =    1.545454545      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.545454545   ) =    0.938881822 = 93.89% [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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