STA2020 - Introductory Statistics & The Probability For Warranty Repair - Statistics Assignment Help

Assignment Task -

2. The manager of a large computer network has developed a probability distribution  for the number of interruptions per day, as shown in the following table. 
No.of Interruptions 0 1 2 3 4 5 6 Probability 0.32 0.35 0.18 0.08 0.04 0.02 0.01 
(a) Compute the expected number of interruptions per day. 
(b) Compute the standard deviation of the number of interruptions per day. 

3. Suppose the warranty records show that the probability that a new computer needs  a warranty repair in the first 90 days is 0.05. A sample of three new computers is  selected. 
(a) What is the probability that none needs a warranty repair? 
(b) What is the probability that one needs a warranty repair? 
(c) What is the probability that at least one needs a warranty repair?

(d) What is the probability that more than one needs a warranty repair? 

4. An important part of the customer service responsibility of a telephone company  relates to the speed with which problems in residential service can be corrected. Suppose past data indicate that the likelihood is 0.7 that a problem in residential  service can be corrected on the same day. Ten problems are reported today. (a) Find the probability that all 10 problems will be corrected today. (b) Find the probability that fewer than four problems will be corrected today. (c) Find the probability that at least five problems will be corrected today. (d) Find the expected number of problems that will be corrected today. (e) Find the standard deviation of the number of problems that will be  corrected today.

5. The number of claims per hour at the WBR Insurance Company has a Poisson  distribution with a mean of 3 claims per hour. Find the probability that in any  given hour there will be 

(a) exactly two claims

(b) at most two claims

(c) three or more claims  

6. The mean number of flaws per 100 metres of fabric produced on a certain  machine at Blanktown Fabrics is 2. If the flaws occur randomly, find the  probability that  

(a) 50 metres of the fabric will have exactly three flaws; 

(b) 200 metres of the fabric will have more than four flaws.

7. The run time for written C-Programmes for Gaussian elimination follows a  normal distribution with a mean of 36 minutes and a standard deviation of 11  minutes. For a C-Programme chosen from Gaussian elimination files at random,  find the probability that the run time will be 

(a) less than 51 minutes

(b) more than 60 minutes 

(c) between 41 and 56 minutes

(d) between 12 and 26 minutes

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