Solved: A manufacturer produces packets of flour whose weights, in grams, can be... [IB Mathematics Analysis and Approaches (AA)]

Question

SLPaper 2

A manufacturer produces packets of flour whose weights, in grams, can be modelled by a normal distribution with mean $1000$ and standard deviation $3.5$ . A packet of flour is rejected for sale if its weight is less than $995$ grams.

Find the probability that a packet selected at random is rejected.

[2]

Verified

Solution

Note: In this question, do not penalise incorrect use of strict inequality signs. Let $X=$ weight of a packet of flour

evidence of identifying the correct area***(M1)*** ${P(X<995)=0.0765637...}$ ${=0.0766}$ A1

[2 marks]

Estimate the number of packets which will be rejected from a random sample of ${100}$ packets.

[1]

Verified

Solution

Note: In this question, do not penalise incorrect use of strict inequality signs. Let $X$ = weight of a packet of flour

$0.0766 \times 100$ $\approx 8$ A1

Note: Accept 7.66.

[1 mark]

Given that a packet is not rejected, find the probability that it has a weight greater than ${1005}$ grams.

[3]

Verified

Solution

Note: In this question, do not penalise incorrect use of strict inequality signs. Let $X$ = weight of a packet of flour

recognition that $P(X > 1005) \cap (X \geq 995)$ is required***(M1)*** $\frac{{P(X \geq 995) \cap (X > 1005)}}{{P(X \geq 995)}}$ $\frac{{P(X > 1005)}}{{P(X \geq 995)}}$ (A1) $\frac{{0.0765637\ldots}}{{1 - 0.0765637\ldots}}$ $= \frac{{0.0765637\ldots}}{{0.923436\ldots}}$ $= 0.0829$ A1

[3 marks]

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