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)
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)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F638e261a-c42c-46ef-873a-8e2d39442a11%2Fee3a6be4-d7f8-45df-9251-04d9d873b2b7%2Fy78rnm_processed.jpeg&w=3840&q=75)
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%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F638e261a-c42c-46ef-873a-8e2d39442a11%2Fee3a6be4-d7f8-45df-9251-04d9d873b2b7%2F9ktpy92r_processed.jpeg&w=3840&q=75)
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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