Directions: For questions 2-4, Use table 2 below. These data contain the concentrations of cholesterol in people at the ages of 20-44 years (sample size = 100) and people at the ages of 45-64 years (sample size = 100). This sheet contains two columns of data, each of which represents the concentration of cholesterol for people in an age category. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest tenth of a decimal place. For example, if you calculate the value as 3.8218, round to 3.8.

1. Complete the frequency table below, listing the concentration of cholesterol.

Table 1. The frequencies of values for cholesterol concentration of people in two age categories: 20-44 years and 45-64 years.
Cholesterol Ranges (mg/dL)	Cholesterol Bins (mg/dL)	Frequency among people at 20-44 years of age	Frequency among people at 45-64 years of age
120-140	140
140-160	160
160-180	180
180-200	200
200-220	220
220-240	240
240-260	260
260-280	280
280-300	300
300-320	320
320-340	340

Table 2

122	137
122	139
126	142
129	151
132	152
137	155
137	161
139	162
143	163
145	166
149	168
149	171
150	173
150	173
150	175
154	177
154	184
155	185
155	186
156	187
158	187
160	188
161	189
162	189
163	189
168	190
169	192
170	194
170	194
172	195
174	197
175	198
175	199
177	200
177	200
178	200
178	200
179	200
180	201
181	202
183	202
184	203
185	204
185	205
185	206
187	207
187	207
188	208
189	210
190	211
191	214
194	215
195	215
198	215
198	216
199	216
200	217
201	218
202	218
202	220
203	221
203	221
205	222
206	223
207	225
209	227
209	229
210	229
211	229
211	232
211	232
212	236
213	240
214	241
214	241
219	243
219	243
220	246
220	246
220	247
226	251
226	251
227	254
228	255
228	256
233	259
236	259
238	264
239	264
241	266
244	268
252	269
254	274
254	279
255	280
265	288
276	296
285	308
288	322
290	331

A)MedianThe MEDIAN requires a list of numbers and Excel returns the median, or central value in a list of values sorted from smallest to largest. The following syntax would be used to compute the median of Variable 1 in the spreadsheet above:

=median(A2:A6)

where the word "median" tells Excel which function to use. The argument in parentheses, A2:A6, tells Excel to use the list of values A2 through A6. For a small sample, we can also list the numbers directly as follows:

=median(5, 3, 7, 4, 6)

In either case, Excel will return a median value of 5, which is the central value in the sorted list 3, 4,5, 6, 7.

B) MinimumThe MIN function requires a list of numbers and returns the minimal value in the list. The following syntax would be used to compute the minimum of Variable 1 in the spreadsheet above:

=min(A2:A6)

C) MaximumThe MAX function requires a list of numbers and returns the maximum value in the list. The following syntax would be used to compute the maximum of Variable 1 in the spreadsheet above:

=max(A2:A6)

D)ModeThe MODE function requires a list of numbers and returns the most frequent value in the list. The following syntax would be used to compute the mode of Variable 1 in the spreadsheet above:

=mode(A2:A6)

Directions: For questions 5-12, use the Data Analysis Workbook and refer to the sheet titled "Q5-12 Descriptive Statistics." These data contain the concentrations of cholesterol in people at the ages of 20-44 years (sample size = 100) and people at the ages of 45-64 years (sample size = 100). This file contains two columns of data, each of which represents the concentration of cholesterol for people in an age category. Use Excel for calculations, modeling, and graphing.

1. Estimate themedian of cholesterol concentration inpeople at 20-44 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4. Median (for people 20-44 years of age) =
2. Estimate theminimumof cholesterol concentration inpeople at 20-44 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4.

Minimum (for people 20-44 years of age) =

1. Estimate themaximum of cholesterol concentration inpeople at 20-44 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4.

Maximum (for people 20-44 years of age) =

1. Estimate themode of cholesterol concentration inpeople at 20-44 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4.

Mode (for people 20-44 years of age) =

1. Estimate themedianof cholesterol concentration inpeople at 45-64 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4.

Median (for people 45-64 years of age) =

1. Estimate theminimum of cholesterol concentration inpeople at 45-64 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4.

Minimum (for people 45-64 years of age) =

1. Estimate themaximum of cholesterol concentration inpeople at 45-64 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4.

Maximum (for people 45-64 years of age) =

1. Estimate themode of cholesterol concentration inpeople at 45-64 years of age. Use Excel for calculations, modeling, and graphing. Round all calculated values to the nearest whole number. For example, if you calculate the value as 3.8218, round to 4.

Mode (for people 45-64 years of age) =

Step 4: For each age category, calculate the probability that a person has high cholesterol.

Now that we know the frequency distribution of cholesterol for people in each age category, we can use the frequencies to infer the probabilities of observing certain values. Recall that the drug company wants to know the probability that a person in a certain age category has high cholesterol (> 240 mg/dL). That way, they can target the appropriate demographic for their drug study.

The probability of an outcome equals therelative frequency of that outcome.

To calculate the relative frequency of high cholesterol, follow these steps:

1. Count the number of people with high cholesterola concentration greater than 240 mg dL. This value equals the frequency.
2. Determine the total number of people in the sample, regardless of their cholesterol concentration. This value equals the sample size.
3. Divide the number of people with high cholesterol (frequency) by the total number of people in the sample (sample size). Convert the resulting value to a percentage by multiplying by 100. This percentage equals the relative frequency. Directions: For questions 13-14, use the Data Analysis Workbook and refer to the sheet titled "Q13-14 Probability Analysis." These data contain the concentrations of cholesterol in people of ages 20-44 years (sample size = 100) and people of ages 45-64 years (sample size = 100). This file contains two columns of data, each of which represents the concentration of cholesterol for people in an age category. Use Excel for calculations, modeling, and graphing.

1. Calculate the probability that a person in the age category of 20-44 years has high cholesterol.Round all calculated values to a whole number. For example, if you calculate the value as 3.8218, round to 4.
2. Calculate the probability that a person in the age category of 45-64 years has high cholesterol.Round all calculated values to a whole number. For example, if you calculate the value as 3.8218, round to 4.

Step 5: Conclude which category of people are more likely to have high cholesterol: people at ages 20-44 years or people at ages 45-64 years.

1. Select the claim that is better supported by the evidence.

A. The drug company should target advertising toward people at 20-44 years of age.

B. The drug company should target advertising toward people at 45-64 years of age.

1. Summarize the evidence that supports your claim, including how you determined whether the drug company should target people at 20-44 years of age or people 45-64 years of age, based on probability. Use quantitative evidence when possible.

Step 6: Consider how you would describe your data with a model.

1. Normal Probability DistributionThis distribution, often called a bell curve, has a single, central mode and a symmetrical tail on each side. The mode is the most probable value.
2. Bimodal Probability DistributionThis distribution has two modes, a lower mode and an upper mode. Both modes may be equally probable.
3. Skewed Probability DistributionThis distribution has a single mode that is shifted to either the left or the right, leaving a long tail on the opposite side. The mode is the most probable value.
4. Uniform Probability DistributionThis distribution is a flat line, such that all values are equally probable. This distribution has no unique mode.

The plots below (A-D) show examples of the four types of probability distributions.

Directions: Use the frequency distributions that you plotted in Step 2 (questions 3-4) to answer questions 17-20.

1. Which of the probability functions best matches the shape of the frequency distribution of cholesterol concentration inpeople between the ages of 20 and 44 years?
   1. normal distribution
   2. bimodal distribution
   3. skewed distribution
   4. uniform distribution
2. Explain your answer to the previous question. Be sure to discuss the features of the frequency distribution that caused you to choose a certain probability distribution.
3. Which of the probability functions best matches the shape of the frequency distribution of cholesterol concentration inpeople between the ages of 45 and 64 years?
   1. normal distribution
   2. bimodal distribution
   3. skewed distribution
   4. uniform distribution
4. Explain your answer to the previous question. Be sure to discuss the features of the frequency distribution that caused you to choose a certain probability distribution.