- You are expected to be familiar with Binomial Distribution. If you took Stat 1124, you would have to study Binomial distribution on your own and refer to the section on Binomial Distribution on page 391-394 of the text before attempting this question.
(a) Suppose a Binomial experiment has a probability of success p given as 0.71 and the number of trials is 25. Use the BINOM.DIST function in Excel to create the distribution function (probability distribution) for the random variable X where X is the number of successes in this experiment. [4 marks]
Answer the following questions, assuming all the conditions of a Binomial experiment are satisfied:
(b) Of the articles from a production line, 16% are defective. If a sample of 20 articles is taken, find the probability that no more than 6 are defective. [2 marks]
(c) Of the articles from a production line, 16% are defective. If a sample of 20 articles is taken, find the expected value and the standard deviation of the random variable defined as the number of defective articles in the sample. [2 marks]
- A discrete random variable X has the probability distribution shown in the table:
x 1 2 3 4
P(X=x)
3/8
1/8
1/4
1/4
Calculate
(a) expected value of X, E(X) [2 marks]
(b) the variance and the standard deviation of X. [2 marks]
- All calculations must be done using Excel. No calculators or tables from your Stat classes should be used.
The number of miles travelled per week by a motorist is normally distributed with a mean of 640 and standard deviation of 50.
(a) Calculate the probability that in a week, he will travel more than 600 miles. [2 marks]
(b) Calculate the probability that in a week, he will travel between 600 and 700 miles. [2 marks]
(c) Calculate the probability that the average number of miles travelled per week over a complete year of 52 weeks will exceed 650. [3 marks]
(d) If the car's gas consumption is 30 miles per gallon, calculate the probability that the motorist will use less than 80 gallons of gas over a period of 4