In Exercises \(9-14, X\) has a normal distribution with the given mean and standard deviation. Find the indicated probabilities. $$ \mu=50, \sigma=10, \text { find } P(30 \leq X \leq 62) $$

IQ Scores IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of \(16 .\) What percentage of the population has an IQ score between 110 and \(140 ?\) (Round your answer to the nearest percentage point.)

A uniform continuous distribution is one with a probability density curve that is a horizontal line. If \(X\) takes on values between the numbers \(a\) and \(b\) with a uniform distribution, find the height of its probability density curve.

Software Testing Exercises \(51-56\) are based on the following information, gathered from student testing of a statistical software package called MODSTAT. \(^{63}\) Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) Find the probability that a student will take at least \(10 \mathrm{~min}\) utes to complete Task \(1 .\)

Assume familiarity with counting arguments and probability (see Section 7.4). \( \text { Camping } \)Kent's Tents has five green knapsacks and fo yellow ones in stock. Curt selects four of them at rando. Let \(X\) be the number of green knapsacks he selects. Give t probability distribution of \(X,\) and find the expected numb of green knapsacks selected.

Following is an excerpt from a full-page ad by MoveOn .org in the New York Times criticizing President G.W. Bush:38 On Tax Cuts: George Bush: "... Americans will keep, thìs year, an average of almost $\$ 1,000$ more of their own money." The Truth: Nearly half of all taxpayers get less than \(\$ 100\). And \(31 \%\) of all taxpayers get nothing at all. The statements referred to as "The Truth" contradict the statement attributed to President Bush-right? Explain.