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### A sample of n=16 observations is drawn from a normal population with µ=1000 and s=200. Find the following. i) P( >1050) ii) P(960< <1050) Part b) (3 marks) An automatic machine in a manufacturing proc

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
...

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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 iii) Z0.2
Part b) (2 marks)
A new car has recently hit the market. The distance travelled on 1 gallon of fuel is
normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find
the probability of the following events.
i) The car travels more than 70 miles per gallon.
ii) The car travels less than 60 miles per gallon.
iii) The car travels between 55 and 70 miles per gallon.
X
X
X
Question 4 [3 marks]
Part a) (1.5 mark)
A random sample of 100 observations was drawn from a population with a standard
deviation of 5. The sample mean was calculated as =400. Estimate the population
mean with 99% confidence.
Part b) (1.5 mark)
A random sample of 5 observations was drawn from a normal population. The sample
same and standard deviation are =175 and s=30. Estimate the population mean with
90% confidence.
Question 5 [3 marks]
Suppose you are using a completely randomized design to study some phenomenon.
There are three treatment levels and a total of 17 people in the study. Complete the
following ANOVA table. Use α=0.05 to find the table F value and use the data to test
the null hypothesis.
Source of Variance SS df MS F
Treatment 26.64
Error 68.42
Total
X
X

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### Solution preview

a) I) P(X>1050) = 1050-1000/200/sqrt(16) )
= 50/200/4 = 50/50 = 1

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