I need clear steps / formulas used with (F) ( I'm lost withcurrent solutions )
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 thatthe IQ of adults is normally distributed with a mean of 100 andstandard deviation of 15. (a) [2 marks] What IQ score distinguishesthe highest 10%? (b) [3 marks] What is the probability that arandomly selected person has an IQ score between 91 and 118? (c) [2marks] Suppose people with IQ scores above 125 are eligible to joina high-IQ club. Show that approximately 4.78% of people have an IQscore high enough to be admitted to this particular club. (d) [4marks] Let X be the number of people in a random sample of 25 whohave an IQ score high enough to join the high-IQ club. Whatprobability distribution does X follow? Justify your answer. (e) [2marks] Using the probability distribution from part (d), find theprobability that at least 2 people in the random sample of 25 haveIQ scores high enough to join the high-IQ club. (f) [3 marks] Let Lbe the amount of time (in minutes) it takes a randomly selectedapplicant to complete an IQ test. Suppose L follows a uniformdistribution from 30 to 60. What is the probability that theapplicant will finish the test in less than 45 minutes?
