Get premium membership and access questions with answers, video lessons as well as revision papers.

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...

      

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.

  

Answers


Mutiso
a) i) Situation 1 is normal distribution. The lifetime is a continuous function, with the mean known and a
standard deviation known. We can only know a given range and not a particular value.
binomial812700.png
c)
i) This is a Poisson distribution since there is a given rate, which is a mean for vehicles passing. In a
large interval, the number of vehicles passing is scattered. The interval is small.
binomial812700i.png
Mutiso answered the question on December 8, 2018 at 04:03


Next: How do you capture the attention of the audience?
Previous: Define probability as used in Quantitative Analysis

View More CPA Quantitative Analysis Questions and Answers | Return to Questions Index


Learn High School English on YouTube

Related Questions