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IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Students

a school district are given an IQ test. If a student is randomly selected (round all probabilities

to 4 decimal places):

a. Find and interpret the probability that they are gifted (IQ of at least 130). Is this unusual?

b. Find and interpret the probability that they have a mental disability (1Q of at most 69). Is this

unusual?

c. Find and interpret the probability that they have a borderline mental disability (IQ of between

70 & 84).

d. Students with the highest 5% of 10's are eligible for the Gifted and Talented program. What is

the cutoff (minimum) score (to the nearest IQ) for eligibility for this program? Interpret

e. Students with the lowest 25% of 10's are eligible for a special intervention program. What is

the maximum score (to the nearest 10) for eligibility for this program? Interpret

f. Students with the middle 30% of 10's will be given a special assessment for potential career

aptitudes. Between what two IQ's (to the nearest IQ) must students have to be given the

assessment? Interpret