91Ó°ÊÓ

The number of hits to a website follows a Poisson process; hits occur at the rate of 1.4 per minute between 7:00 p.m. and 9:00 p.m. Compute the probability that the number of hits between 7:30 p.m. and 7:35 p.m. is (a) exactly seven. Interpret the result. (b) fewer than seven. Interpret the result. (c) at least seven. Interpret the result.

Determine whether the distribution is a discrete probability distribution. If not, state why. $$ \begin{array}{cc} x & P(x) \\ \hline 1 & 0 \\ \hline 2 & 0 \\ \hline 3 & 0 \\ \hline 4 & 0 \\ \hline 5 & 1 \\ \hline \end{array} $$

The phone calls to a computer software help desk occur at the rate of 2.1 per minute between 3:00 p.m. and 4:00 p.m. Compute the probability that the number of calls between 3:10 p.m. and 3:15 p.m. is (a) exactly eight. Interpret the result. (b) fewer than eight. Interpret the result. (c) at least eight. Interpret the result.

Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why. Three cards are selected from a standard 52 -card deck with replacement. The number of kings selected is recorded.

The potholes on a major highway in the city of Chicago occur at the rate of 3.4 per mile. Compute the probability that the number of potholes over 3 miles of randomly selected highway is (a) exactly seven. Interpret the result. (b) fewer than seven. Interpret the result. (c) at least seven. Interpret the result. (d) Would it be unusual for a randomly selected 3 -mile stretch of highway in Chicago to contain more than 15 potholes?

Determine the required value of the missing probability to make the distribution a discrete probability distribution. $$ \begin{array}{cc} x & P(x) \\ \hline 3 & 0.4 \\ \hline 4 & ? \\ \hline 5 & 0.1 \\ \hline 6 & 0.2 \\ \hline \end{array} $$

Determine the required value of the missing probability to make the distribution a discrete probability distribution. $$ \begin{array}{ll} x & P(x) \\ \hline 0 & 0.30 \\ \hline 1 & 0.15 \\ \hline 2 & ? \\ \hline 3 & 0.20 \\ \hline 4 & 0.15 \\ \hline 5 & 0.05 \\ \hline \end{array} $$

In Problems \(17-28,\) a binomial probability experiment is conducted with the given parameters. Compute the probability of \(x\) successes in the \(n\) independent trials of the experiment. $$ n=10, p=0.4, x=3 $$

Televisions In the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable \(X\) represents the number of televisions in households. $$ \begin{array}{cl} \text { Number of Televisions, } x & P(x) \\ \hline 0 & 0 \\ \hline 1 & 0.161 \\ \hline 2 & 0.261 \\ \hline 3 & 0.176 \\ \hline 4 & 0.186 \\ \hline 5 & 0.116 \\ \hline 6 & 0.055 \\ \hline 7 & 0.025 \\ \hline 8 & 0.010 \\ \hline 9 & 0.010 \\ \hline \end{array} $$ (a) Verify this is a discrete probability distribution. (b) Draw a graph of the probability distribution. Describe the shape of the distribution. (c) Determine and interpret the mean of the random variable \(X\). (d) Determine the standard deviation of the random variable \(X\). (e) What is the probability that a randomly selected household has three televisions? (f) What is the probability that a randomly selected household has three or four televisions? (g) What is the probability that a randomly selected household has no televisions? Would you consider this to be an impossible event?

In the following probability distribution, the random variable \(X\) represents the number of marriages an individual aged 15 years or older has been involved in. $$ \begin{array}{ll} x & P(x) \\ \hline 0 & 0.272 \\ \hline 1 & 0.575 \\ \hline 2 & 0.121 \\ \hline 3 & 0.027 \\ \hline 4 & 0.004 \\ \hline 5 & 0.001 \end{array} $$ (a) Verify that this is a discrete probability distribution. (b) Draw a graph of the probability distribution. Describe the shape of the distribution. (c) Compute and interpret the mean of the random variable \(X\). (d) Compute the standard deviation of the random variable \(X\). (e) What is the probability that a randomly selected individual 15 years or older was involved in two marriages? (f) What is the probability that a randomly selected individual 15 years or older was involved in at least two marriages?