Suppose that the IQ of adults is normally distributed with amean of 100 and standard deviation of 15. not sure with currentsolution posted, personally it wasn't clear step by step working. Iget lost with some values that he gets ( not sure where he getsthem )
here's the question:
To get full marks for the following questions you need toconvert the question from words to a mathematical expression (i.e.use mathematical notation), defining your random variables wherenecessary, and using correct probability statements.
Suppose that the IQ of adults is normally distributed with amean of 100 and standard deviation of 15.
(a) [2 marks] What IQ score distinguishes the highest 10%?
(b) [3 marks] What is the probability that a randomly selectedperson has an IQ score between
91 and 118?
(c) [2 marks] Suppose people with IQ scores above 125 areeligible to join a high-IQ club. Show that approximately 4.78% ofpeople have an IQ score high enough to be admitted to thisparticular club.
(d) [4 marks] Let X be the number of people in a random sampleof 25 who have an IQ score high enough to join the high-IQ club.What probability distribution does X follow? Justify youranswer.
(e) [2 marks] Using the probability distribution from part (d),find the probability that at least 2 people in the random sample of25 have IQ scores high enough to join the high-IQ club.
(f) [3 marks] Let L be the amount of time (in minutes) it takesa randomly selected applicant to complete an IQ test. Suppose Lfollows a uniform distribution from 30 to 60. What is theprobability that the applicant will finish the test in less than 45minutes?
