Please explain how you got the answer. Thank you. The scale of scores on an IQ t

Question

Please explain how you got the answer. Thank you.

The scale of scores on an IQ test is approximately Normal with mean 97 and standard deviation 11. The organization MENSA, which calls itself the high lQ society, " requires an IQ score of 130 or higher for membership. Use this information to answer the following questions. What proportion of adults would qualify for membership? (Use 4 decimal places.) Corinne scored 118 on her lQ test. Her z-score is about (Use 2 decimal places.) Corinne scored 118 on her lQ test. She scored higher than what percent of all adults? (Use 2 decimal places.)

Explanation / Answer

for normal distribution z=(X-mean)/std deviation

a) P(X>130)=1-P(X<130)=1-P(Z<(130-97)/11)=1-P(Z<3)=1-0.99865=0.0013

b)z score =(118-97)/11 =21/11=1.91

c)P(Z<1.91)=0.97

hence 97 percentage

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