Sharks. Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites:

Length	18.7	12.3	18.6	16.4	15.7	18.3	14.6	15.8	14.9	17.6	12.1
Length	16.4	16.7	17.8	16.2	12.6	17.8	13.8	12.2	15.2	14.7	12.4
Length	13.2	15.8	14.3	16.6	9.4	18.2	13.2	13.6	15.3	16.1	13.5
Length	19.1	16.2	22.8	16.8	13.6	13.2	15.7	19.7	18.7	13.2	16.8

(a) Examine these data for shape, center, spread, and outliers. The distribution is reasonably Normal except for one outlier in each direction. Because these are not extreme and preserve the symmetry of the distribution, use of the t procedures is safe with 44 observations.

(b) Give a 95% confidence interval for the mean length of great white sharks. Based on this interval, is there significant evidence at the 5% level to reject the claim "Great white sharks average 20 feet in length"?

(c) Before accepting the conclusions of (b), you need more information about the data. What would you like to know?

Construct and interpret a 95% confidence interval for the mean length of great white sharks. Based on this interval, is there significant evidence at the 5% level to reject the claim "Great white sharks average 20 feet in length"? Justify your answer.

The heights of adult American men can be modeled by a normal distribution with mean $\mu=69$ inches and standard deviation $\sigma=2.5$ inches. Use the empirical rule to answer the question below.

What percent of adult American men are greater than 74 inches tall?

The dotplot shows the number of calories per serving for 16 brands of frozen cheese pizza. Identify any outliers in the distribution.

Here are the lengths in feet of 44 great white sharks:

Use your calculator to construct a normal probability plot. Interpret this plot.

Here are the lengths in feet of 44 great white sharks:

9.4, 12.1, 12.2, 12.3, 12.4, 12.6, 13.2, 13.2, 13.2, 13.2, 13.5,

13.6, 13.6, 13.8, 14.3, 14.6, 14.7, 14.9, 15.2, 15.3, 15.7, 15.7,

15.8, 15.8, 16.1, 16.2, 16.2, 16.4, 16.4, 16.6, 16.7, 16.8, 16.8,

17.6, 17.8, 17.8, 18.2, 18.3, 18.6, 18.7, 18.7, 19.1, 19.7, 22.8

Use the following summary statistics to calculate the percent of data values within 1,2 , and 3 standard deviations of the mean. How closely do the results match the empirical rule?

$$\begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{n} & \text { Mean } & \text { SD } & \text { Min } & {Q}_1 & \text { Med } & {Q}_{\mathbf{3}} & \text { Max } \\ \hline 44 & 15.586 & 2.55 & 9.4 & 13.55 & 15.75 & 17.2 & 22.8 \\ \hline \end{array}$$

Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites:

It isn't clear exactly what parameter $\mu$ you estimated in (b). What information do you need to say what $\mu$ is?

Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites:

Examine these data for shape, center, spread, and outliers. The distribution is reasonably normal except for one outlier in each direction. Because these are not extreme and preserve the symmetry of the distribution, use of the $t$ procedures is safe with 44 observations.

Here are a stemplot and numerical summaries of the percents of residents aged 65 and older in the 50 states and the District of Columbia. Is this distribution approximately normal? Justify your answer based on the graph and the empirical rule.

$$\begin{array}{l|ll} 10 & 45 & \\ 11 & 6 & \\ 12 & 0 & \\ 13 & 146 & \\ 14 & 4566689 & \\ 15 & 00000111345678 & \\ 16 & 01111223455789 & \text{Key: } 16 \mid 2 \text{ represents} \\ 17 & 01457 & \text{a state in which} \\ 18 & 18 & 16.2\% \text{ of residents} \\ 19 & 49 &\text{are } 65 \text{ and older.} \\ \end{array}$$

$$\begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{n} & \text { Mean } & \text { SD } & \text { Min } & Q_1 & \text { Med } & {Q}_{\mathbf{3}} & \text { Max } \\ \hline 51 & 15.54 & 1.90 & 10.4 & 14.8 & 15.6 & 16.5 & 19.9 \\ \hline \end{array}$$

Following is a stemplot of the percents of residents aged 65 and older in the 50 states and the District of Columbia.

$$\begin{array}{r|l} 7 & 7 \\ 8 & \\ 9 & 0 \\ 10 & 379 \\ 11 & 44 \\ 12 & 02333445899 \\ 13 & 02234555557788889 \\ 14 & 012334445689 \\ 15 & 49 \\ 16 & 0 \\ 17 & 3 \end{array}$$

KEY: 12|2 represents a state in which 12.2% of residents are 65 and older. Which value appears to be an outlier? Can you guess what state this is?

The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. How long do the longest 20% of pregnancies last?

Where do the young live? Here is a stemplot of the percent of residents aged 25 to 34 in each of the 50 states:

$$\begin{array}{l|ll} 11 & 44 \\ 11 & 66778 \\ 12 & 0134 \\ 12 & 666778888 \\ 13 & 0000001111444 \\ 13 & 7788999 & \\ 14 & 0044 \\ 14 & 567 \\ 15 & 11 \\ 15 & \\ 16 & 0 \end{array}$$

Give an appropriate key for this stemplot.

As part of a study of salmon health, researchers measured the pH of 25 salmon fillets. Here are the data:

6.22 6.24 6.25 6.26 6.26 6.31 6.32 6.32 6.32 6.33 6.34 6.36 6.36

6.37 6.38 6.39 3.39 6.42 6.43 6.44 6.45 6.48 6.48 6.52 6.53

Based on your answers to the previous parts, is the distribution of pH for these salmon approximately normal? Explain your answer.

Refer to the earlier exercise. About 0.15% of 14-year-old boys have cholesterol levels less than what value? Justify your answer.