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1)A manufacturer receives a certain component from a supplier in shipments of 100 units

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1)A manufacturer receives a certain component from a supplier in shipments of 100 units. Two units in each

shipment are selected at random and tested. If either one of the units is defective the shipment is rejected.

Suppose a shipment has 5 defective units.

a.Construct the probability distribution for the number

of defective units in such a sample.

b.Find the probability that such a shipment will be accepted.

2) According to a study, 90% of K-12 schools or districts in a country use digital content such as ebooks, audio books, and digital books. Of these 90%, 9 out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district use digital content and uses it as part of their curriculum.

3) Of 83 adults selected randomly from one town, 63 have health insurance.

Find a 90% confidence interval for the proportion of all adults in the town who have health insurance.
A. 0.682 to 0.836
B. 0.650 to 0.868
C. 0.638 to 0.880
D. 0.667 to 0.851

4) Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.

Guessing the first digit in the price of a car

 

Sample space is { }

There are _ outcomes in the sample space

5) A study found that people who suffer from obstructive sleep apnea

are at increased risk of having heart disease. Identify the two events described in the study. Do the results indication taht the events are independent of dependent?

6) Use the frequency distribution, which shows the number of American

voters (in millions) according to age, to find the probability that a voter chosen at random is in the 18 to 20 years old range.
Ages Frequency
18 to 20 4.6
21 to 24 8.9
25 to 34 20.3
35 to 44 25.5  (45 to 64 51.1
65) and over 27.3

7) Discuss the following and give real life examples.

Why do we have a Margin of Error in Statistics? If statistics are meant to be accurate, why are they sometimes accompanied by an estimate of doubt?

What is the relationship between Margin of Error, Confidence interval and Sample Size.

 

8) The Jarque-Bera Normality test which is used to determine if residuals on a model are

normally distributed is the most important test in ensuring reliability of a regression model. Critically evaluate this statement.