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 sample that are chicken is the same as the proportion of the pies made that day that are chicken. On Monday Milo calculated that he needed exactly 4 chicken pies in his sample. (a) Work out the total number of chicken pies that were made on Monday. On Tuesday, the number of steak pies Milo needs in his sample is 6 correct to the nearest whole number. Milo takes at random a pie from the 450 pies made on Tuesday. (b) Work out the lower bound of the probability that the pie is a steak pie.

GCSE Edexcel Maths Rounding, Estimation & Bounds: A factory makes 450 pies every d

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 sa... show full transcript

Worked Solution & Example Answer:A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

Step 1

(a) Work out the total number of chicken pies that were made on Monday.

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Answer

To find the total number of chicken pies made on Monday, we can use the following proportion:

Let the total number of chicken pies made be denoted as $x$ . According to the question, the proportion of chicken pies in the sample is the same as the proportion of chicken pies made overall.
We know that Milo took a sample of 15 pies, which included 4 chicken pies. Therefore, the proportion of chicken pies in the sample is:

$ext{Proportion of chicken pies in sample} = \frac{4}{15}$

Setting this equal to the proportion of chicken pies made:

$\frac{4}{15} = \frac{x}{450}$

Cross-multiplying gives:

$4 \times 450 = 15 \times x$

$1800 = 15x$

Dividing both sides by 15:

$x = \frac{1800}{15} = 120$

Thus, the total number of chicken pies made on Monday is 120.

Step 2

(b) Work out the lower bound of the probability that the pie is a steak pie.

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Answer

On Tuesday, Milo needs 6 steak pies in his sample, correct to the nearest whole number. This means that the actual number of steak pies can be as low as 5.5 and as high as 6.5. Thus, the lower bound for the number of steak pies needed is 6 - 0.5 = 5.5. We round this in whole numbers:

The maximum number of steak pies he could pick is 6. Therefore, we take:

$\text{Lower bound of steak pies} = 6$

To find the lower bound for the probability of picking a steak pie, we first need to determine the number of chicken pies made, which is:

$\text{Total pies} = 450 - \text{Number of chicken pies}$
From part (a), we found that 120 chicken pies were made, so:

$\text{Number of steak pies} = 450 - 120 = 330$

Thus, the lower bound probability that the pie is a steak pie would be:

$\text{Probability} = \frac{330}{450} = \frac{11}{15} \approx 0.7333$

The lower bound of the probability that the pie is a steak pie is approximately 0.7333.

A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

Worked Solution & Example Answer:A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

(a) Work out the total number of chicken pies that were made on Monday.

(b) Work out the lower bound of the probability that the pie is a steak pie.

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