The correct answer by the standard deviation would be as follow:
i. less than 0.052kg - 288 eggs
ii. between 0.052 and 0.075kg) - 1476 eggs
III greater than 0.075 - 36 eggs
Given:
number of the samples, n = 1800 eggs
the mean of the distribution, m = 0.06 kg
standard deviation, d = 0.009 kg
(i) less than 0.052 kg (standard size):
1 standard deviation below the mean = m - d
m - d = 0.06 kg - 0.009 kg = 0.051 kg
(the standard size is 1 standard deviation below the mean)
less than 1 standard deviation below the mean in a normal distribution is = 16% of the given samples
Number of standard size = 0.16 x 1800
= 288 eggs
(ii) Between 0.052 kg and 0.075kg (medium size):
0.052 kg is 1 standard deviation below the mean
2 standard deviations above the mean:
> m + 2d
> m + 2d
> 0.06 + 2(0.009)
= 0.078 kg
Between 1 standard deviation below the mean and 2 standard deviation above the mean in a normal distribution
= (68 + 14)%
= 82%
Number of medium size = 0.82 x 1800
= 1,476 eggs
(iii) Greater than 0.075 kg (large size):
0.078 kg is 2 standard deviations below the mean
greater than 2 standard deviation above the mean in a normal distribution = 2 % of the number of given samples
Number of large size = 0.02 x 1800
= 36 eggs
Learn more about standard devaiation:
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