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During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points.

a. What is the probability distribution for X?

b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X.

c. Use your calculator to find the probability that DeAndre scored with 60 of these shots.

d. Find the probability that DeAndre scored with more than 50 of these shots

Explain in complete sentences what the confidence interval means.

One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of $151$hours each month with a standard deviation of $32$hours. Assume that the underlying population distribution is normal.

Identify the following:

a. $\overline{x}$=_______

b. $s_x$=_______

c. n =_______

d. n – 1 =_______

Use the following information to answer the next six exercises: One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of $151$hours

each month with a standard deviation of $32$hours. Assume that the underlying population distribution is normal.

Identify the following:

a.$\overline{x}=\_\_\_\_\_\_\_$

b.$s_x=\_\_\_\_\_\_\_$

c.$n=\_\_\_\_\_\_\_$

d.$n–1=\_\_\_\_\_\_\_$

Define the random variable X in words.

Define the random variable $\stackrel{¯}{X}$in words.

Which distribution should you use for this problem?

Construct a $99\%$confidence interval for the population mean hours spent watching television per month.

(a) State the confidence interval

(b) sketch the graph, and

(c) calculate the error bound.

Why would the error bound change if the confidence level were lowered to$95\%$?

The data in the Table are the result of a random survey of $39$national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let $X=$the number of colors on a national flag.

$\begin{array}{|cc|}\hline \mathit{x}& \text{Freq.}\\ 1& 1\\ 2& 7\\ 3& 18\\ 4& 7\\ 5& 6\\ \hline\end{array}$

Construct a$95\%$confidence interval for the true mean number of colors on national flags.

How much area is in both tails (combined)?