Assignment
Answer all the questions.
1. If Project A has the following probability distribution of forecast profits:
Prob : 0.1 0.3 0.4 0.2
Profit/ Loss : -800 -200 400 500
Should he invest in project A or not? Why?
2. Assuming that the customer arrivals at the Fidelity Credit Union drive through window are Poisson distributed with a mean of five per hour , find
a. The probability that in a given hour more than eight customers will arrive at the drive-through window.
b. The probability that between three and six customers inclusive, will arrive at the drive through window in a given hour.
c. The probability that fewer than three customers will arrive at the window in a given 30 minute period.
3. A small southern West Australian country town has maintained records showing that the daily maximum temperature during summer (Dec.,Jan.,Feb.) has averaged 30 degree Celsius with a standard deviation of 5 degree Celsius. Further, the maximum temperature appears to be approximately normally distributed.
Find:
(a) the percentage of summer days that will have a maximum temperature between 30C & 35C.
(b) the percentage of days that the maximum temperature will exceed 37.5 C
(c) the probability that the maximum temperature will be less than 24 C.
(d) the proportion of summer days that the maximum temperature will be between 18C and 20C
(e) The maximum temperature that will be exceeded only 5% of the time.
4. Explain the different types of probability and non-probability sampling techniques.
5. The general manager of Western Software Pty Ltd believes that 30% of the firm’s orders come from new or first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of new or first-time customers. The results of the sample will be used to verify the general manager’s claim of p = 0. 30.
(a) Assume that the general manager is correct and p = 0.30, what is the sampling distribution of p for this study.
(b) What is the probability that the sample proportion p will be between 0.2 and 0.4?
(c) What is the probability that the sample proportion will be within plus or minus 0.05 of the population proportion p = 0.30?