A packing plant fills bags with cement - Edexcel - A-Level Maths Statistics - Question 7 - 2008 - Paper 2

To find the weight that is exceeded by 99% of the bags, we need to determine the 1st percentile of the distribution.

Using the Z-table, we find that the Z-score corresponding to 0.01 is approximately -2.326.

Now we can find the actual weight:

$x = \mu + Z \cdot \sigma = 50 + (-2.326) \cdot 2 = 45.3474.$
Thus, the weight that is exceeded by 99% of the bags is approximately 45.35 kg.

We found earlier that P(X > 53) = 0.0668 and therefore P(X < 53) = 1 - P(X > 53) = 0.9332.

Now, we are looking for the probability for two bags weighing more than 53 kg and one weighing less:

Using the binomial probability formula:

$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$

We have:

• n = 3 (total bags)
• k = 2 (bags more than 53 kg)
• p = 0.0668

Calculating:

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