Question

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





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Answer 1

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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