Recall that scores on the Wechsler IQ test are normally distributed with mean 100 points and standard deviation 15 points. If a prisoner has a low enough IQ, it is against the law to sentence the prisoner to death. Florida used to have an inflexible cutoff of 70 points to decide whether prisoners were too intellectually disabled to be executed. But on May 27, 2014, the Supreme Court ruled that Florida and nine other states need to have a flexible cutoff, like other states do. A cut- off as high as 75 points is used for some prisoners, depending on their behavior and history.
a. Find the probability that a randomly selected person (not necessarily a prisoner) has an IQ less than 70 points.
b. Find the probability that a randomly selected person (not necessarily a prisoner) has an IQ less than 75 points.
c. As of the ruling, there were 392 Florida prisoners on death row. Assume there would have been 9 additional prisoners on death row, but their IQs were lower than 70. Estimate the greatest number of prisoners that could be removed from death row due to the ruling.
d. Describe any assumptions that you made in calculating your estimate in part (c).