Question

Question 1
a). i. To estimate the average time it takes to assemble a certain printer component,
the industrial engineer at an electronics firm timed 40 technicians in the performance
of this task, getting a mean of 12.73 minutes and a standard deviation of 2.06
minutes. Construct a 98% confidence interval for the true average time it takes to
assemble the printer component.
ii. A sample of 16 girls gave a mean mass of 35 kg and a standard deviation of 6 kg.
Assuming normality, construct a 96% confidence interval for ?.
iii. A random sample of 20 students obtained a mean of 72 and variance of 16 on a
Mathematics examination. Assuming the scores to be normally distributed, construct a
98% confidence interval for?^2

b. Briefly explain the following:
i) Critical Region
ii) Confidence Coefficient
iii) Alternative Hypothesis
c. A car manufacturer claims that the average weekly income of owners of his car is
$180. An investigator takes a sample of 200 such car owners and finds out that they
have an average weekly income of $184.26 with a standard deviation of $24.12. On
the basis of the sample, do you agree with the manufacturer’s claim?
Test at ? = 5%

Question 2
The masses of packages from a particular machine are normally distributed
with a mean of 200g and a standard deviation of 2g. Find the probability that a
randomly selected package from the machine weighs:
i. Less than 197g
ii. More than 200.5g
iii. Between 198.5 and 199.5g
b) X ~N(-8,12). Find:
i. P(X< -9.8)
ii. P(X > -8.2)
iii. P(-7 < X < 0.5)
Question 2
a. Briefly explain each of the following:
i. Null Hypothesis
ii. Alternative Hypothesis
iii. Critical Region
iv. Type I error
v. Type II error
vi. Significance level
Question 3
a. Let X have the Binomial Distribution with parameters n=8 and p=0.1.
i. What is the set of all possible values of X?
ii. Find:
α.) P(X≥ 7)
β.) P(X<1)
Ȣ.) P(X≥ 1)
b. In a large city, 10% of the people are smokers. A random sample of five (5)
persons is drawn from the city. Find the probability that in this sample:
i. None is a smoker
ii. At least one is a smoker
iii. Four are smokers
iv. Between 1 and 3 both inclusive are smokers.

Question 4
In the study of a certain aquatic organism, large number of samples were taken from a
pond, and the number of organisms in each sample counted. The average number of
organisms per sample was 2. Assuming that the number of organisms follows a Poisson
distribution, find the probability that the next sample taken will contain
a) one or few organisms
b) Exactly 3 organisms
c) More than 5 organisms

Question 5
a) The weekly amount spent for the maintenance and repairs of a waste
management company was observed over a long period of time to be
approximately normally distributed with a mean of ¢300 and a standard deviation
of ¢15.
I. If ¢350 is budgeted for the week, what is the probability that the actual costs
will be less than the budgeted amount.
II. What is the probability that the amount spent on a particular week will be
between ¢270 and ¢400.

Answer 1

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