In: Statistics and Probability
Suppose that the IQ of adults is normally distributed with a mean of 100 and standard deviation of 15. not sure with current solution posted, personally it wasn't clear step by step working. I get lost with some values that he gets ( not sure where he gets them )
here's the question:
To get full marks for the following questions you need to convert the question from words to a mathematical expression (i.e. use mathematical notation), defining your random variables where necessary, and using correct probability statements.
Suppose that the IQ of adults is normally distributed with a mean 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 selected person has an IQ score between
91 and 118?
(c) [2 marks] Suppose people with IQ scores above 125 are eligible to join a high-IQ club. Show that approximately 4.78% of people have an IQ score high enough to be admitted to this particular club.
(d) [4 marks] Let X be the number of people in a random sample of 25 who have an IQ score high enough to join the high-IQ club. What probability distribution does X follow? Justify your answer.
(e) [2 marks] Using the probability distribution from part (d), find the probability that at least 2 people in the random sample of 25 have IQ scores high enough to join the high-IQ club.
(f) [3 marks] Let L be the amount of time (in minutes) it takes a randomly selected applicant to complete an IQ test. Suppose L follows a uniform distribution from 30 to 60. What is the probability that the applicant will finish the test in less than 45 minutes?