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Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given as in Table $4.34$

On average, how many years do you expect it to take for an individual to earn a $B.S.$?

People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given in the following table. There is a five-video limit per customer at this store, so nobody ever rents more than five DVDs.

$\begin{array}{|ll|}\hline x& P\left(x\right)\\ 0& 0.03\\ 1& 0.50\\ 2& 0.24\\ 3& \\ 4& 0.07\\ 5& 0.04\\ \hline\end{array}$

1. Describe the random variable X in words.
2. Find the probability that a customer rents three DVDs.
3. Find the probability that a customer rents at least four DVDs.
4. Find the probability that a customer rents at most two DVDs.

Another shop, Entertainment Headquarters, rents DVDs and video games. The probability distribution for DVD rentals per customer at this shop is given as follows. They also have a five-DVD limit per customer.

$\begin{array}{|ll|}\hline \mathit{x}& \mathit{P}\left(\mathit{x}\right)\\ 0& 0.35\\ 1& 0.25\\ 2& 0.20\\ 3& 0.10\\ 4& 0.05\\ 5& 0.05\\ \hline\end{array}$

e. At which store is the expected number of DVDs rented per customer higher?

f. If Video to Go estimates that they will have 300 customers next week, how many DVDs do they expect to rent next week? Answer in sentence form.

g. If Video to Go expects 300 customers next week, and Entertainment HQ projects that they will have 420 customers, for which store is the expected number of DVD rentals for next week higher? Explain.

h. Which of the two video stores experiences more variation in the number of DVD rentals per customer? How do you know that?

What is the probability the baker will sell exactly one batch? $P(x=1)$ = _______

Florida State University has $14$statistics classes scheduled for its Summer $2013$term. One class has space available for $30$students, eight classes have space for $60$students, one class has space for $70$students, and four classes have space for $100$students.

a. What is the average class size assuming each class is filled to capacity?

b. Space is available for $980$students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable $X$equal the size of the student’s class. Define the PDF for $X$.

c. Find the mean of $X$.

d. Find the standard deviation of$X$.

In a lottery, there are $250$prizes of $\backslash (5,50$prizes of $\backslash )25$, and ten prizes of $\$100$. Assuming that $10,000$tickets are to be issued and sold, what is a fair price to charge to break even?

According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per $1,000$babies in a healthy baby nursery. The number climbs to an average of $30$per $1,000$babies in an intensive care nursery.

Suppose that $1,000$babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies were born deaf.

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.
Define the random variable and list its possible values.

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.

State the distribution of $X$.

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.

Find the probability that at least four of the $25$patients actually have the flu.

According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per $1,000$babies in a healthy baby nursery. The number climbs to an average of $30$per $1,000$babies in an intensive care nursery. Suppose that $1,000$babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies were born deaf.

On average, for every$25$patient calling in, how many do you expect to have the flu?