Question

3. Now consider your cleaned data in reference to the Armspan variable/factor of the student data. Notice that this data is categorized as quantitative, continuous, and ratio level in type. (This portion of the activity is Based on Workshop Statistics, Rossman, p. 66) a. In the area to the right, copy the Armspan data values (again take the cleaned data set of 96 values) and then sort them in order from least to greatest. From this column of Armspan values, create an appropriate frequency table with exactly 5 classes--remember, we did such frequency charts back in Unit 1. For the next part, b, you may choose to produce the histogram graph at the same time. Finally extend your frequency table to include a relative frequency (probability) column. Answer is to D. Produce a histogram for your frequency table (if you did not do so as you constructed your table in part a). Does the distribution of the Armspan values appear to be roughly normal?Explain your answer briefly c. Compute the mean and standard deviation of the Armspan values...not from the frequency table as done in the discrete case above but as done in the first unit, but this time assuming this is sample data of all stats students. Sample mean, xbar (X) Sample std. deviation, s d. Determine the proportion of the students in this sample whose armspan is at most 155 cm. e. Suppose that the armspans in the population of all university students taking elementary statistics do in fact follow a perfect normal distribution though our group did not with the population mean μ-198.8 cm and population s andard deviation σ 12.2 cm . Under this assumption, determine the proportion of all students who have a armspan measure of at most 155 cm. (HINT: this calculation is related to the concepts covered in text section 8-41)

146.0
149.0
151.0
151.0
152.0
152.5
153.0
153.5
154.0
154.5
155.0
155.0
156.0
156.0
156.0
158.5
159.0
159.0
160.0
160.0
160.0
160.5
161.0
161.0
161.0
162.0
162.0
162.5
163.0
163.0
163.0
165.0
165.0
165.5
165.5
166.0
166.0
166.5
167.0
167.0
167.5
167.5
167.5
167.5
168.0
169.0
169.0
169.0
169.5
170.0
170.0
170.5
170.5
172.0
172.0
172.0
172.5
172.5
173.0
173.0
173.5
173.5
174.0
174.5
175.0
175.0
175.0
175.0
175.5
176.0
176.5
176.5
177.0
177.0
178.0
180.0
180.0
180.5
181.0
183.0
183.0
185.0
185.0
185.5
186.0
187.0
187.0
188.0
188.0
188.0
189.5
191.0
192.0
192.5
194.0
195.5

Answer 1

A)

Frequency Table Class 146-155.9 156-165.9 166-175.9 176-185.9 186-195.9 Count 12 23 34 15 12

B)

35- 30 25 34 23 2 20 15 12 12 10 146 156 166 176 186 196 Histogram(Frequency Diagram)

yes, the distribution look normal

C)

mean = 169.99479

sd = 11.61136

d)

there are 12 who are at most 155

hence required proportion = 12/(12+23+34+15+12) = 12/96 = 0.125

P(X < 155)
= P(Z < ( 155 - 198.8)/12.2)
= P(Z < -3.5901)
= 0.00165