The lengths in millimetres (mm) of 60 runner beans taken from a particular crop were measured and found to be normally distributed. The runner beans were given ID numbers and their lengths to the nearest millimetre are recorded in the table below. a) Select a sample of 12 runner beans using systematic sampling and the random number 4 for the first selection. Write your sample in a table with headings, as demonstrated below. Runner bean ID Length (mm)

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The lengths in millimetres (mm) of 60 runner beans taken from a particular crop were
measured and found to be normally distributed. The runner beans were given ID
numbers and their lengths to the nearest millimetre are recorded in the table below.
a) Select a sample of 12 runner beans using systematic sampling and the random
number 4 for the first selection. Write your sample in a table with headings, as
demonstrated below.
Runner bean ID
Length (mm)
Lengths of runner beans (mm)
Runner bean Length(mm)
Runner bean
Length(mm)
Runner bean
Length(mm)
ID Number
ID Number
ID Number
150
21
156
41
201
165
22
182
42
165
3
179
23
166
43
177
4
153
24
200
44
210
181
25
185
45
189
205
26
203
46
187
198
27
195
47
188
8.
171
28
170
48
179
9
210
29
180
49
142
10
168
30
210
50
175
11
186
31
194
51
175
12
179
32
188
52
177
13
188
33
160
53
190
14
175
34
189
54
162
146
35
170
55
187
15
172
36
189
56
168
16
164
37
167
57
167
17
160
38
178
58
187
18
152
39
197
59
166
19
40
210
60
204
20
209
Transcribed Image Text:The lengths in millimetres (mm) of 60 runner beans taken from a particular crop were measured and found to be normally distributed. The runner beans were given ID numbers and their lengths to the nearest millimetre are recorded in the table below. a) Select a sample of 12 runner beans using systematic sampling and the random number 4 for the first selection. Write your sample in a table with headings, as demonstrated below. Runner bean ID Length (mm) Lengths of runner beans (mm) Runner bean Length(mm) Runner bean Length(mm) Runner bean Length(mm) ID Number ID Number ID Number 150 21 156 41 201 165 22 182 42 165 3 179 23 166 43 177 4 153 24 200 44 210 181 25 185 45 189 205 26 203 46 187 198 27 195 47 188 8. 171 28 170 48 179 9 210 29 180 49 142 10 168 30 210 50 175 11 186 31 194 51 175 12 179 32 188 52 177 13 188 33 160 53 190 14 175 34 189 54 162 146 35 170 55 187 15 172 36 189 56 168 16 164 37 167 57 167 17 160 38 178 58 187 18 152 39 197 59 166 19 40 210 60 204 20 209
Using your sample from part a), answer the following questions. Make sure you use the
correct notation.
b) Find the mean length.
c) Find the standard deviation. Round your answer to 2 decimal places.
d) Find the variance. Round your answer to 1 decimal place.
The grower knows from experience that the standard deviation of the population for this
crop of runner beans is 16.6 millimetres.
e) Using your sample mean from part b), find a 95% confidence interval for the
mean length of the population of runner beans. Round your answers to 1
decimal place.
f) State the width of the 95% confidence interval in part e).
g) Comment on how the width of this confidence interval will be affected if the
confidence level is increased to 99%.
Transcribed Image Text:Using your sample from part a), answer the following questions. Make sure you use the correct notation. b) Find the mean length. c) Find the standard deviation. Round your answer to 2 decimal places. d) Find the variance. Round your answer to 1 decimal place. The grower knows from experience that the standard deviation of the population for this crop of runner beans is 16.6 millimetres. e) Using your sample mean from part b), find a 95% confidence interval for the mean length of the population of runner beans. Round your answers to 1 decimal place. f) State the width of the 95% confidence interval in part e). g) Comment on how the width of this confidence interval will be affected if the confidence level is increased to 99%.
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