QTB – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

Question

The weights of bags of Pando Yam produced by Swallow Company Limited are normally distributed with a mean of 3,020 grams and a standard deviation of 4 grams.

Required:
i. If a bag is picked at random, what is the probability that it weighs:

Less than 3,012 grams? (4 marks)
ii. Between 3,012 grams and 3,021.6 grams? (6 marks)
Show all the relevant normal distribution diagrams.

Answer

(i) 3012 grams is below the mean

That is, 3012 grams is 2 standard deviations below the mean (fig b(i))
∴ From the table, Z = 2 gives 0.4772 or 47.72% of the distribution to be
within two standard deviations below the mean
∴ P(Z < -2) = 0.5 – 0.4772 = 0.0288
∴ The probability of a bag of Pando yam being less than 3012 grams is
0.0228

(ii) – 3012 grams is below the mean:

3021.6 grams is above the mean

We are interested in the area of the normal curve between 2 standard
deviations below the mean and 0.4 standard deviation above the man.

(fig b(ii))
∴From the table
Z = – 2 (below the mean), probability = 0.4772
Z = 0.4 (above the mean), probability = 0.1554
This gives the total probability as 0.6326
That is , there is a 0.6326 or 63.23% chance that a bag of Pando yam picked at
random will lie between 3012 grams and 3021.6 grams.