20 Hassan produces apple juice using apples grown on his farm.
He has 180 apple trees.
Each tree produces 40 kilograms of apples per year.
To make 1 litre of apple juice, Hassan needs 2.5 kilograms of apples.
He sells his apple juice in 0.75 litre bottles.
Work out how many bottles of apple juice Hassan can expect to produce in one year.​

a (i) The number of standard size is 288 eggs

a (ii) The number of medium size is 1,476 eggs

a (iii) The number of large size is 36 eggs

b (i) The expected profit made from selling the standard size is Gh¢43.2

b (ii) The expected profit made from selling the medium size is Gh¢516.6

b (iii) The expected profit made from selling the large size is Gh¢16.2

The given parameters:

the mean of the distribution, m = 0.06 kg

standard deviation (std) of the distribution, d = 0.009 kg

number of the samples, n = 1800 eggs

(i) Find the position of "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 equal to 16% of the data samplesNumber of standard size = 0.16 x 1800 = 288 eggs

(ii) Find the position of "Between 0.052 kg and 0.075kg (medium size)":

0.052 kg is 1 standard deviation below the mean2 standard deviation above the mean = m + 2dm + 2d = 0.06 + 2(0.009) = 0.078 kg

(the medium size is between 1 std below the mean and 2 std above the mean)

Between 1 std below the mean and 2 std above the mean in a normal distribution = (68 + 14)% = 82%Number of medium size = 0.82 x 1800 = 1,476 eggs

(iii) Find the position of "Greater than 0.075 kg (large size)":

0.078 kg is 2 standard deviation below the meangreater than 2 std above the mean in a normal distribution = 2 % of the data samples Number of large size = 0.02 x 1800 = 36 eggs

Check: 288 eggs + 1476 eggs + 36 eggs = 1,800 eggs

(b) the cost of production of an egg = Gh¢0.45

the selling price of the standard size = Gh¢0.60

the selling price of the medium size = Gh¢0.80

the selling price of the large size = Gh¢0.95

(i) The expected profit made from selling the standard size:

Profit = total revenue - cost of production

Profit = 288(0.6) - 288(0.45) = Gh¢43.2

(ii) The expected profit made from selling the medium size:

Profit = total revenue - cost of production

Profit = 1476(0.8) - 1476(0.45) = Gh¢516.6

(iii) The expected profit made from selling the large size:

Profit = total revenue - cost of production

Profit = 36(0.9) - 36(0.45) = Gh¢16.2

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