3.
a) No of unfilled bottles in random sample of:
i) 10 bottles – 6 RF = 6/10 = 0.6
ii) 50 bottles - 17 RF = 17/50 = 0.34
iii) 200 bottles – 62 RF = 62/200 = 0.31
The sample of 200 bottles produces RF = 0.31 which is the closes to the predicted % in Q2 part a)
0.3085. Results are consistent when it comes to the sample of 200 bottles but not with 10 and 50 bottles
samples.
b) Number of bottles within 1 standard deviation:
10 bottles – 8 RF = 8/10 = 0.8
50 bottles – 37 RF = 37/50 = 0.74
200 bottles – 130 RF = 130/200 = 0.65
Number of bottles within 2 standard deviation:
10 bottles – 10 RF = 10/10 = 1
50 bottles – 47 RF = 47/50 = 0.94
200 bottles – 190 RF = 190/200 = 0.95
Number of bottles within 3 standard deviation:
10 bottles – 10 RF = 10/10 = 1
50 bottles – 49 RF = 49/50 = 0.98
200 bottles – 199 RF = 199/200 = 0.995
According to the Empirical rule, 68% of data should lie within 1, 95% within 2, and 99.7% within 3.
200 bottles samples is the most consistent with the empirical rule values. 65% within 1, 95% within 2,
99.5% within 3.
c) The general shape of the pattern is a straight line. It follows a normal distribution.
