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A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1
Question 13
A factory makes 450 pies every day. The pies are chicken pies or steak pies. Each day Milo takes a sample of 15 pies to check. The proportion of the pies in his sam... show full transcript
Worked Solution & Example Answer:A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1
Step 1
Work out the total number of chicken pies that were made on Monday.
Answer
Milo samples 15 pies, and he needs 4 chicken pies in that sample.
To find the proportion of chicken pies in the sample:
Since the proportion in the sample is the same as that in the total production, we can equate:
To find the number of chicken pies made, we cross-multiply:
Thus, the total number of chicken pies made on Monday is 120.
Step 2
Work out the lower bound of the probability that the pie is a steak pie.
Answer
On Tuesday, Milo needs 6 steak pies, correct to the nearest whole number. This means the actual number of steak pies (N) could be between:
- Lower bound: 6 - 0.5 = 5.5
- Upper bound: 6 + 0.5 = 6.5
Given that he samples 15 pies again, the number of steak pies in the total 450 pies can be calculated:
Total steak pies = Total pies - Number of chicken pies = 450 - 120 = 330
This leads us to find the lower bound of steak pies needed:
Taking the lower bound of steak pies count being 6 at 5.5, we calculate:
Thus, the lower bound probability that the pie is a steak pie is approximately 0.7333.