Question

The mean weight of 500 bags of beans at a certain store is 151 kg and the standard deviation is 15 kg. Assuming that the weights are normally distributed, find how many bags weigh

i. between 120 and 155 kg

ii. more than 185 kg. (3 marks)

Answer 1

find the number of standard deviations that the weights are from the mean

...this is the z-score

for 120 kg bags ... (151 - 120) / 15 = 2.067 ... below the mean
... from the z-score table ... 1.94% of the bags are below this value

for 155 kg bags ... (155 - 151) / 15 = 0.267 ... above the mean
... from the z-score table ... 60.54% of the bags are below this value

so ... (60.54 - 1.94)% of the 500 bags are between 120 kg and 155 kg