Question 1

Paper 2Hard6 marks

A snack company models the mass, XX g, of a packet as normally distributed with mean 503503 g and standard deviation 4.84.8 g. Packets with mass below 494494 g do not meet the lower specification. The company wants at least 94%94\% of packets to meet the specification 494≤X≤U494\leq X\leq U where UU is the upper specification.

Use your GDC for normal probability and inverse normal calculations.

(a)

Show that P(X<494)=0.0304P(X<494)=0.0304

[2]
(b)

Using your result from part (a), determine the smallest value of UU to the nearest 0.10.1 g, that meets the company’s requirement. A manager proposes setting UU to the 95th percentile of the distribution. Assess whether this proposal meets the requirement.

[4]

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