#### Question Preview:

A sample of n=16 observations is drawn from a normal population with µ=1000 and
σ=200. Find the following.
i) P( >1050)
ii) P(960< <1050)
Part b) (3 marks)
An automatic machine in a manufacturing process is operating properly if the lengths
of an important subcomponent are normally distributed with mean=117cm and standard
deviation =5.2 cm.
i) Find the probability that one selected subcomponent is longer than 120cm.
ii) Find the probability that if four subcomponents are randomly selected, their mean
length exceeds 120cm.
Question 2 [5 marks]
Part a) (2 marks)
...

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#### Question Preview:

A sample of n=16 observations is drawn from a normal population with µ=1000 and
σ=200. Find the following.
i) P( >1050)
ii) P(960< <1050)
Part b) (3 marks)
An automatic machine in a manufacturing process is operating properly if the lengths
of an important subcomponent are normally distributed with mean=117cm and standard
deviation =5.2 cm.
i) Find the probability that one selected subcomponent is longer than 120cm.
ii) Find the probability that if four subcomponents are randomly selected, their mean
length exceeds 120cm.
Question 2 [5 marks]
Part a) (2 marks)
Calculate the statistic, set up the rejection region, draw the sampling distribution and
interpret the result,
H0: µ=50
H1: µ<50
Given that: σ=15, n=100, =48, α=0.05.
Part b) (3 marks)
A business student claims that, on average, an MBA student is required to prepare more
than five cases per week. To examine the claim a professor asks a random sample 10
MBA student to report the number of cases they prepare weekly; the professor
calculates the mean value and standard deviation, which is 6 and 1.5, respectively. Can
the professor conclude at the 5% significance level that the claim is true, assuming that
the number of case is normal distribution?
Question 3 [4 marks]
Part a) (2 marks)
Find the following probabilities by checking the z table
i) P((Z>-0.8)
ii) P(-0.85

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