[ASK]Probability Distributions of Discrete Variables

[Hafiz Bachtiar]

1. Under normal operating conditions 1.5% of the transistors produced in a factory are defective. An inspector takes a random sample of forty transistors and finds that two are defective.

a. What is the probability that exactly two transistors will be defective from a random sample of forty under normal operating conditions?

b. What is the probability that more than two transistors will be defective from a random sample of forty if conditions are normal?

 

2. A control system is set up so that when production conditions are normal, only 6% of items from the production line gives readings beyond a particular limit. If more tha two of six successive items are beyond the limit, production is stopped and all machine settings are examined. What is the probability that production will be stopped in this way when production conditions are normal?

 

3. A company supplying transistors claims that they produce no more than 2% defectives. A purchaser picks 50 at random from an order of 5000 and tests the 50. If he finds more than 1 defective, he rejects the order. If the supplier’s calim is true and 2% of the transistors are defective, what is the probablity that the order will be rejected?

 

4. An experiment was conducted wherein three balls were drawn at random from a barrel containing two blue balls, three red balls, and five green balls. We want to find the mean and variance of the probability distribution of the number of green balls chosen. Explain why this problem involving three colours can not be handled using a binomial distribution. Suppose we consider both the blue balls and the red balls together as not-green. Now find the required mean and variance.

 

5. The number of cars entering a ssmall parking lot is a random variable having a Poisson distribution with a mean of 1.5 per hour. The lot holds only 12 cars.

a. Find the probability that the lot fills up in the first hour (assuming that all cars stay in the lot longer than one hour).

b. Find the probability that more than 3 cars arrive between 9 am and 11 am.

 

6. Customers arrive at a checkout counter at an average rate of 1.5 per minute. What distribution will apply reasonable assumptions are made? List those assumptions. Find the probabilities that

a. Exactly two will arrive in any given minute;

b. At least three will arrive during an interval of two minutes;

c. At most 13 will arrive during an interval of six minutes.

[imatfaal]

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So Hafiz would you explain where you have got to in solving this problem and what has stopped your progress - hopefully members can then help you to overcome your difficulties yourself.