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Question 4​(4 marks) It may be assumed that the length of nails produced by a particular...

Question 4​
It may be assumed that the length of nails produced by a particular machine is a normally distributed random variable with mean 4.62cm. We have collected the following random sample of lengths of nails: 4.63 cm, 4.59 cm, 4.64 cm, 4.62 cm, 4.66 cm and 4.69 cm.
a) Find the standard error of the sample mean .
b) What is the sampling distribution of ? State any assumptions you need to make.
c) What is the probability that we observe this sample mean or a higher value?
d) What would the sampling distribution be if the nails produced by this machine are not normally distributed? What would you suggest?
Math   Statistics-And-Probability   
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