Most tests that give IQ scores are designed to have a mean of 100 and a standard

Question

Most tests that give IQ scores are designed to have a mean of 100 and a standard deviation of 15. IQ testing is one way in which people are categorized as having different levels of intellectual disability (the category formerly known as mental retardation). Prior to DSM-V, when the term mental retardation was used, four categories were distinguished. Two of those categories are shown below:

-IQ of 20-35 (in combination with impaired life skills): severe mental retardation

-IQ of 50-70 (in combination with impaired life skills): mild mental retardation

People with scores above 70 were not considered to have mental retardation. The IQ test was used first, and then, if a person’s score fell into the range for mental retardation (70 or below) above, that person would be assessed for life skill impairments. What percentage of people would be expected to have IQ scores that might put them into the severe mental retardation range? Assume that IQ scores are normally distributed in the population.

Explanation / Answer

To be in severe mental retardation range, IQ score must be between 20 and 35

Mean = 100

Standard deviation = 25

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

P(20 < X < 35) = P(X < 35) - P(X < 20)

= P(Z < (35 - 100)/15) - P(Z < (20 - 100)/15

= P(Z < -4.33) - P(Z < -5.33)

= 0.000007 - 5x10-8

= 6.95x10-6

= 0.000695 %

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

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