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Suppose that one in five customers buy product Y. If four customers are chosen at random:
(i) what is the probability that none of them buy product Y?
(ii) what is the probability that at least three of them buy product Y?
Let the sample size of the television tube brightness experiment be ten and the sample mean and sample standard deviation be 315.4 microamps and 13.6 microamps, respectively. Suppose that the design engineer claims that this tube will require at least 300 microamps of current to produce the desired brightness level.

Choose an appropriate hypothesis to test.

H0: mu =

_________, H1: mu ( >, <, not equal) _________

Find the P-value for this test.

A. 0.25 < P-value < 0.50
B. 0.0005 < P-value < 0.0010
C. 0.0025 < P-value < 0.0050
D. 0.025 < P-value < 0.050

With a significance level of a = 0.05 ( fail to reject, reject ) H0.

For this test, we assumed that the underlying distribution of the data is a t-distribution.
A. True
B. False
An article in Fortune (September 21, 1992) claimed that nearly one-half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving either an M.S. or a Ph.D. degree. Data from an article in Engineering Horizons (Spring 1990) indicate that 117 of 484 new engineering graduates were planning graduate study.

1. Test the hypothesis H0 : p=0.5 versus H1: p is not equal to 0.5. Usea a = 0.05

A. Fail to reject H0
B. Reject H0

2. What is the P-value for this test? Round your answer to 4 decimal places. Enter your answer in accordance to the question statement

The 2004 presidential election exit polls from the critical state of Ohio provided the following results. There were 2020 respondents in the exit polls and 768 were college graduates. Of the college graduates, 412 voted for George Bush.


(a) Calculate a 99% confidence interval for the proportion of college graduates in Ohio that voted for George Bush. Round the answers to 3 decimal places.


(b) Calculate a 95% lower confidence bound for the proportion of college graduates in Ohio that voted for George Bush. Round the answer to 3 decimal places.


Assume 20% of people have a flu immunisation at the start of winter . Suppose that 5% of people who have a flu immunisation will contract the flu and that 30% of those who don’t have a flu immunisation will contract the flu

What proportion of people will contract the flu ?

Paras Ltd. issued 40000, 11% debentures of 100 rupees each on 1st April 2015. Half of the debentures were due for redemption on 31st March 2019. The company decided to transfer the minimum required amount to Debenture Redemption Reserve on 31st March, 2018 and invested the necessary amount in debenture Redemption Investments on 30th April, 2018. Pass the necessary journal entries for Redemption of Debentures.


Suppose that the operations manager of a nose mask packaging delivery service is contemplating the purchase of a new fleet of trucks during this COVID-19 period. When packages are efficiently stored in the trucks in preparation for delivery, two major constraints have to be considered. The weight in pounds and volume in cubic feet for each item. Now suppose that in a sample of 200 packages the average weight is 26.0 pounds with a standard deviation of 3.9 pounds. In addition suppose that the average volume for each of these packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the variation of the weight and volume
For a set of 15 observations the mean came out to be 17.3. Later on checking it is
discovered that an observation 19.5 was incorrectly recorded whereas the correct value was
15.9. Calculate the correct mean from these information.

A population of N=15 scores has a mean of u=8  One score in the population is changed from X=20 to X=5. What is the value for the new population mean?


in a multiple choice test there are 10 questions for each question there is a choice of 4 answers only one of the which is correct. a student guesses at each of the answers, if he needs to obtain over half mark to pass, and the question carry equal weight, find the probability that he passes
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