Practice Problems (Continuous Probability Distributions)

IQ scores are normally distributed with a mean of µ = 100 and standard deviation of σ = 15

1. Tim Cook (new CEO for Apple) wants to implement a new HR strategy where only very highly intelligent people are employed at Apple. The first stage of his strategy is to only hire new employees if their IQ is above the 90^th percentile. What is the minimum IQ score needed to get hired at Apple? In other words, what score is at the 90^th percentile (separates the top 10% from the remainder of the distribution)?

2. The second stage of Tim's strategy is to begin "phasing out" employees, starting with those who have an IQ at or below the 15^th percentile.What is the minimum IQ score current employees need to keep their job? In other words, what score is at the 15^th percentile (separates the bottom 15% from the remainder of the distribution)?

3. After failed attempts to recruit employees with an IQ in the 90^th percentile, Tim Cook lowers his standards to the 70^th percentile. What is the new minimum IQ score needed to get hired at Apple?

4. After realizing that the IQ standards for getting phased out are too low, Tim Cook raises his standard for employees who will not get phased out to those with an IQ that is in the 25^th percentile or higher. What is the new minimum IQ score needed to keep your job at Apple?

IQ scores are normally distributed with a mean of µ = 100 and standard deviation of σ = 15

Laura just took an IQ test and is curious about the proportion of test takers who fall into certain categories, based on the mean and standard deviation for the IQ test:

5. Candidates for the Mensa Club (for geniuses) must score above 133 to belong. What is the probability that test any given taker would make it into the club? p (x > 133)?

6. According the Wechsler IQ testing agency, a "Moron" is anyone scoring from 41 - 55. What is the probability that a randomly selected test taker would be considered a Moron?

7. According the Wechsler IQ testing agency, a person with an IQ of 40 or below is an Idiot. What proportion of IQ test takers are Idiots?

8. According the Wechsler IQ testing agency, a person with an IQ 40 or below is an Idiot. What proportion of test takers are not Idiots?