# Maths Statistics Question

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Thread starter 1 year ago
#1
A machine puts crisps into packets.
The weight of crisps in each packet, M grams follows a normal distribution with mean 40 g

Given that 20% of packets contain more than 42 g of crisps,

(a) Find, to 2dp, the value of k such that P(k < A < 40) = 0.40

Eighteen packets of crisps are selected at random.
(b) Find the probability that fewer than 3 of these packets contain more than 42 g or crisps.

A second machine makes larger packets of crisps of weight Y grams, where Y is normally distributed with standard deviation 7.5 g

A manager believes that the mean weight of crisps put into each packet is greater than 175 g

A random sample of 10 packets from this second machine was found to have a mean weight of crisps of 178.5 g

(c) Test whether or not the mean weight of crisps in larger packets, filled by the second machine, is greater than 175 g
State your hypotheses clearly and use a 5% level of significance.
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1 year ago
#2
To start you need to find the standard deviation by using "Given that 20% of packets contain more than 42 g of crisps" in standard normal distribution.
You are then able to do part a with the mean and standard deviation you have worked out.
Part c is hypothesis tests
Last edited by RLH17; 1 year ago
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1 year ago
#3
part b : use the binomial distribution
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1 year ago
#4
(Original post by the bear)
part b : use the binomial distribution
what would you need to put in as p, x and n?
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1 year ago
#5
(Original post by kimw0001)
what would you need to put in as p, x and n?
what would you suggest ?

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1 year ago
#6
(Original post by the bear)
what would you suggest ?

n =18 , not sure about p or x
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1 year ago
#7
(Original post by kimw0001)
n =18 , not sure about p or x
n is good.

for p you are looking for a suitable probability of one success. then you need to apply that for x successes.
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1 year ago
#8
(Original post by the bear)
n is good.

for p you are looking for a suitable probability of one success. then you need to apply that for x successes.
how do i find p?
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1 year ago
#9
(Original post by kimw0001)
how do i find p?
just read through the first part of the question.
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