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Maths please help (Statistics Normal Distrubution)

(1300U40-1)
4
A company produces kettlebells whose weights are normally distributed with mean 16 kg
and standard deviation 0.08 kg.
a) Find the probability that the weight of a randomly selected kettlebell is greater than
16.05 kg. [2]
The company trials a new production method. It needs to check that the mean is still
16 kg. It assumes that the standard deviation is unchanged. The company takes a random
sample of 25 kettlebells and it decides to reject the new production method if the sample
mean does not round to 16 kg to the nearest 100 g.
b) Find the probability that the new production method will be rejected if, in fact, the
mean is still 16 kg.
The company decides instead to use a 5% significance test. A random sample of 25
kettlebells is selected and the mean is found to be 16.02 kg.
c) Carry out the test to determine whether or not the new production method will be
rejected

Please help, I'm trying so hard to understand this question and I only really understand part a. Is there anyone that can help explain it to me, I got an exam and I really want to ace it
Reply 1
Original post by iamour
(1300U40-1)
4
A company produces kettlebells whose weights are normally distributed with mean 16 kg
and standard deviation 0.08 kg.
a) Find the probability that the weight of a randomly selected kettlebell is greater than
16.05 kg. [2]
The company trials a new production method. It needs to check that the mean is still
16 kg. It assumes that the standard deviation is unchanged. The company takes a random
sample of 25 kettlebells and it decides to reject the new production method if the sample
mean does not round to 16 kg to the nearest 100 g.
b) Find the probability that the new production method will be rejected if, in fact, the
mean is still 16 kg.
The company decides instead to use a 5% significance test. A random sample of 25
kettlebells is selected and the mean is found to be 16.02 kg.
c) Carry out the test to determine whether or not the new production method will be
rejected

Please help, I'm trying so hard to understand this question and I only really understand part a. Is there anyone that can help explain it to me, I got an exam and I really want to ace it

Part b) onwards is pretty much the usual hypothesis test for the sample mean. You should have covered it, but some tlmathsvdioes at
https://sites.google.com/view/tlmaths/home/a-level-maths/full-a-level/o-hypothesis-testing/o3-sample-means-hypothesis-testing

Part b) is slightly different as you want to get something related to
P(15.95<X<16.05)
but thats similar to part a)
(edited 11 months ago)

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