91Ó°ÊÓ

Give an example of a real-life situation that can be modeled by a random variable with a probability distribution whose histogram is highest on the left.

Mensa is a club for people with high IQs. To qualify, you must be in the top \(2 \%\) of the population. One way of qualifying is by having an IQ of at least 148 , as measured by the Cattell intelligence test. Assuming that scores on this test are normally distributed with a mean of 100 , what is the standard deviation? HINT [Use the table in the Appendix "backwards."]

What is the after-tax income range of approximately \(99.7 \%\) of all Swedes?

How wide should the bars in a histogram be so that the area of each bar equals the probability of the corresponding range of values of \(X\) ?

Under what assumptions are the estimates in the empirical rule exact?

Must the expected number of times you hit a bull's-eye after 50 attempts always be a whole number? Explain.

How wide should the bars in a histogram be so that the probability \(P(a \leq X \leq b)\) equals the area of the corresponding portion of the histogram?

If \(X\) is a continuous random variable, what values can the quantity \(P(X=a)\) have?

Which is larger for a continuous random variable, \(P(X \leq a)\) or \(P(X

Give at least one scenario in which you might prefer to model the number of pages in a randomly selected book using a continuous random variable rather than a discrete random variable.