Question 7 - A-Level Maths

Exam Board	AQA
Module	S1 (Statistics 1)
Year	2015
Session	June
Marks	4
Topic	Normal Distribution
Type	Direct comparison of probabilities

The weight of a sack of mixed dog biscuits can be modelled by a normal distribution with a mean of 10.15 kg and a standard deviation of 0.3 kg . A pet shop purchases 12 such sacks that can be considered to be a random sample.
Calculate the probability that the mean weight of the 12 sacks is less than 10 kg .
The weight of dry cat food in a pouch can also be modelled by a normal distribution. The contents, $x$ grams, of each of a random sample of 40 pouches were weighed. Subsequent analysis of these weights gave $$\bar { x } = 304.6 \quad \text { and } \quad s = 5.37$$
1. Construct a $99 \%$ confidence interval for the mean weight of dry cat food in a pouch. Give the limits to one decimal place.
2. Comment, with justification, on each of the following two claims. Claim 1: The mean weight of dry cat food in a pouch is more than 300 grams.
  Claim 2: All pouches contain more than 300 grams of dry cat food.
  [0pt] [4 marks]
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