The mass of the eggs laid by a certain breed of hen is normally distributed random variable with mean 0.06kg and standard deviation 0.009kg. if a random sample of 1800 eggs are sold, how many would you expect to have mass i. less than 0.052kg
ii. between 0.052 and 0.075kg)
III greater than 0.075

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

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