Get premium membership and access questions with answers, video lessons as well as revision papers.
Normal distribution can be used as an approximation to the binomial distribution when the number considered is large, n>30, np (product of number and probability of success) and nq (product
of number and probability of failure) are greater or equal to 5.
Mutiso answered the question on December 14, 2018 at 13:34
- Give some examples of the type of data that form a normal distribution(Solved)
Give some examples of the type of data that form a normal distribution.
Date posted: December 14, 2018. Answers (1)
- A manager is convinced that a new type of machine does not affect production at the
company's major shop floor. In order to test this, 12...(Solved)
A manager is convinced that a new type of machine does not affect production at the
company's major shop floor. In order to test this, 12 samples of this week's hourly output is
taken and the average production per hour is measured as 1158 with a standard deviation of 71. The
output per hour averaged 1196 before the machine was introduced.
Required:
Test the manager's conviction
Date posted: December 14, 2018. Answers (1)
- Prior to an advertising campaign, 35 per cent of a sample of 400 housewives used a certain product.
After the campaign, 40 per cent of a...(Solved)
Prior to an advertising campaign, 35 per cent of a sample of 400 housewives used a certain product.
After the campaign, 40 per cent of a second sample of 400 housewives used the same product.
Required:
Did the campaign increase sales?
Date posted: December 14, 2018. Answers (1)
- Two researchers in marketing, Catherine Mbugua and George Otieno, reviewed the theory of product
life cycle with respect to a specific product. They conducted a research...(Solved)
Two researchers in marketing, Catherine Mbugua and George Otieno, reviewed the theory of product
life cycle with respect to a specific product. They conducted a research project to determine the
applicability of the theory to popular music records. As part of the study, they collected extensive
information on a sample of 12 music records judged on the basis of certain well-defined criteria to be successes and a sample of 10 music records to be failures. They collected data on each music record for
a period of 16 weeks from the date the record was released to the market. One item of information they
collected on each music record was radio airplay. Measurement of this variable yielded the following
means and standard deviations for the two samples of music records.
ii) What assumptions are we making in order to use the pooled estimate of the common population
variance?
Date posted: December 14, 2018. Answers (1)
- If a Type II error is costly but a Type I error is not, why should you set the level of significance $\alpha$ at 0.10,...(Solved)
If a Type II error is costly but a Type I error is not, why should you set the level of significance $\alpha$ at 0.10, 0.20 or even higher?
Date posted: December 14, 2018. Answers (1)
- What is wrong with the following hypotheses?(Solved)
What is wrong with the following hypotheses?
Date posted: December 14, 2018. Answers (1)
- What is a one-sided confidence interval? When is it necessary?(Solved)
What is a one-sided confidence interval? When is it necessary?
Date posted: December 14, 2018. Answers (1)
- The General Manager of a large hotel in Bombay wishes to know whether or not the personal services
provided to its customers are uniform throughout the...(Solved)
The General Manager of a large hotel in Bombay wishes to know whether or not the personal services
provided to its customers are uniform throughout the hotel industry. Whether the clients in the less
expensive rooms get the same service as that of clients of more expensive rooms. The data collected from the comment cards is tabulated below:
Were the customers treated differently according to their room charges? Test the hypothesis at 0.05 level of significance.
Date posted: December 14, 2018. Answers (1)
- Two different models are available for the same machine. The production statistics (number of units
produced per hour) of these two models are given below. The...(Solved)
Two different models are available for the same machine. The production statistics (number of units
produced per hour) of these two models are given below. The data was collected on different days.
Will you conclude that Model A and Model B have the same productivity?
Date posted: December 8, 2018. Answers (1)
- The sales Manager of a large sales force is interested in finding whether or not average number of weekly
sales contacts per sales representative (15) has...(Solved)
The sales Manager of a large sales force is interested in finding whether or not average number of weekly
sales contacts per sales representative (15) has changed. The sample information was collected and it was
found that 200 sales representatives had an average of 16.5 contacts per week with a standard deviation of
3.5. At 5 per cent level of significance, what should the sales manager conclude?
Date posted: December 8, 2018. Answers (1)
- Suppose it is known that the mean annual income of workers in a certain community is Rs.5,000 with a
standard deviation of Rs.1,200. A researcher suspects...(Solved)
Suppose it is known that the mean annual income of workers in a certain community is Rs.5,000 with a
standard deviation of Rs.1,200. A researcher suspects the “son of soil” workers have higher than the average income. He draws a random sample of 144 local workers and obtains the sample mean of Rs.5,500. Can he say the local workers have significantly higher income than the total population?
Date posted: December 8, 2018. Answers (1)
- KK accounting firm has noticed that of the companies it audits, 85% show no inventory shortages, 10%
show small inventory shortages and 5% show large inventory...(Solved)
KK accounting firm has noticed that of the companies it audits, 85% show no inventory shortages, 10%
show small inventory shortages and 5% show large inventory shortages. KK firm has devised a new
accounting test for which it believes the following probabilities hold:
P (Company will pass test/no shortage) = 0.90
P (Company will pass test/small shortage) = 0.50
P (Company will pass test/large shortage) = 0.20
Required:
i) Determine the probability if a company being audited fails this test has large or small inventory
shortage.
ii) If a company being audited passes this test, what is the probability of no inventory shortage?
Date posted: December 8, 2018. Answers (1)
- Define probability as used in Quantitative Analysis(Solved)
Define probability as used in Quantitative Analysis.
Date posted: December 8, 2018. Answers (1)
- In each of the following three situations, use binomial, poisson, or normal distribution depending on which is the most appropriate.
In each case, explain why you...(Solved)
In each of the following three situations, use binomial, poisson, or normal distribution depending on which is
the most appropriate.
In each case, explain why you selected the distribution and draw attention to any feature which supports or
casts doubt on the choice of distribution.
a) Situation 1:
The lifetimes of a certain type of electrical components are distributed with a mean of 800 hours and
standard deviation of 160 hours.
Required:
i) Identify situation 1.
ii) If the manufacturer replaces all the components that fail before the guaranteed minimum lifetime of
600 hours, what percentage of the components have to be replaced?
iii) If the manufacturer wishes to replace only 1% of the components that have the shortest life, what
value should be used as the guaranteed lifetime?
iv) What is the probability that the mean lifetime of a sample of 25 of these electrical components exceeds 850 hours?
b) Situation 2:
A green grocer buys peaches in large consignments directly from wholesaler. In view of the perishable
nature of the commodity, the green grocer accepts that 15% of the supplied peaches will usually be
unsaleable. As he cannot check all the peaches individually, he selects a single batch of 10 peaches on
which to base his decision of whether to purchase a large consignment or not. If no more than two of
these peaches are unsatisfactory, the green grocer purchases the consignment.
Required:
i) Identify situation 2.
ii) Determine the probability that under normal supply conditions, the consignment is purchased.
c) Situation 3:
Vehicles pass a certain point on a busy single-lane road at an average rate of two per 10 second interval.
Required:
i) Identify situation 3.
ii) Determine the probability that more than three cars pass this point during a 20 second interval.
Date posted: December 8, 2018. Answers (1)
- What is Bayes Theorem? Explain how Bayes Theorem can be utilized practically.(Solved)
What is Bayes Theorem? Explain how Bayes Theorem can be utilized practically.
Date posted: December 7, 2018. Answers (1)
- What is the addition rule of probability and for what type of events is it valid?(Solved)
What is the addition rule of probability and for what type of events is it valid?
Date posted: December 7, 2018. Answers (1)
- Under what conditions does P (A/B) = P (A)?(Solved)
Under what conditions does P (A/B) = P (A)?
Date posted: December 7, 2018. Answers (1)
- The purchasing department has analysed the number of orders placed by each of the 5 departments in the
company by type of this financial year as...(Solved)
The purchasing department has analysed the number of orders placed by each of the 5 departments in the
company by type of this financial year as given in the table below:
An error has been found in one of these orders.
Required:
i) Determine the probability that the incorrect order was not for consumables.
ii) Determine the probability that the incorrect order came from maintenance or production.
iii) Calculate the probability that the incorrect order was an equipment order from purchase.
Date posted: December 7, 2018. Answers (1)
- In a particular life insurance office, employees Simiyu, Juki, Waithera and Baraza have a diploma, with
Simiyu and Baraza also having a degree. Simiyu, Macharia, Waithera,...(Solved)
In a particular life insurance office, employees Simiyu, Juki, Waithera and Baraza have a diploma, with
Simiyu and Baraza also having a degree. Simiyu, Macharia, Waithera, Thuo, Mwanzia and Kungu are
associate members of the Chartered Insurance Institute (ACII) with Thuo and Mwanzia having a diploma.
Required:
Identifying set A as those employees with diploma, set C as those employees who are ACII and set D as
having a degree:
i) Specify the elements of sets A, C and D.
ii) Draw a Venn diagram representing sets A, C and D, together with their known elements.
iii) What special relationship exists between sets A and D?
iv) Specify the elements of the following sets and for each set, state in words what information is being
conveyed: A C; D C and D C .
v) What will be a suitable universal set for this situation?
Date posted: December 7, 2018. Answers (1)
- Explain briefly some of the advantages of the standard normal distribution(Solved)
Explain briefly some of the advantages of the standard normal distribution.
Date posted: December 7, 2018. Answers (1)