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Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. $$\begin{array}{|c|c|}\hline x & {P(x)} \\ \hline 1 & {0.15} \\ \hline 2 & {0.35} \\ \hline 3 & {0.40} \\ \hline 4 & {0.10} \\ \hline\end{array}$$ What is the probability the baker will sell exactly one batch? \(P(x=1)=\)_________

Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. $$\begin{array}{|c|c|}\hline x & {P(x)} \\ \hline 1 & {0.15} \\ \hline 2 & {0.35} \\ \hline 3 & {0.40} \\ \hline 4 & {0.10} \\ \hline\end{array}$$ On average, how many batches should the baker make?

Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time. Construct a PDF table.

Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for at least one event each month. \(P(x>0)=\)________

Identify the mistake in the probability distribution table. $$\begin{array}{|c|c|c|}\hline x & {P(x)} & {x^{*} P(x)} \\ \hline 1 & {0.15} & {0.15} \\ \hline 2 & {0.25} & {0.40} \\ \hline 3 & {0.25} & {0.85} \\\ \hline 4 & {0.20} & {0.85} \\ \hline 5 & {0.15} & {1} \\ \hline\end{array}$$

Use the following information to answer the next six exercises: On average, a clothing store gets 120 customers per day. What is the probability of getting 35 customers in the first four hours? Assume the store is open 12 hours each day.

You buy a lottery ticket to a lottery that costs \(\$ 10\) per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one \(\$ 500\) prize, two \(\$ 100\) prizes, and four \(\$ 25\) prizes. Find your expected gain or loss.

Use the following information to answer the next four exercises. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. On average, for every 25 patients calling in, how many do you expect to have the flu?

Use the following information to answer the next two exercises: The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13-year win history of 382 wins out of 1,034 games played (as of a certain date). An upcoming monthly schedule contains 12 games. The expected number of wins for that upcoming month is: a. 1.67 b. 12 c. \(\frac{382}{1043}\) d. 4.43 Let \(X =\) the number of games won in that upcoming month.

Use the following information to answer the next two exercises: The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13-year win history of 382 wins out of 1,034 games played (as of a certain date). An upcoming monthly schedule contains 12 games. Six different colored dice are rolled. Of interest is the number of dice that show a one. a. In words, define the random variable \(X.\) b. List the values that \(X\) may take on. c. Give the distribution of \(X . X \sim\) _____(___,___) d. On average, how many dice would you expect to show a one? e. Find the probability that all six dice show a one. f. Is it more likely that three or that four dice will show a one? Use numbers to justify your answer numerically.