Question

1] Assume that the helium porosity (in percentage) of coal sample taken from any particular seam is normally distributed with true standard deviation 0.75.

(a) Compute a 90% confidence interval for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.

(b) How large a sample size is necessary if the width of the 95% interval for the true average is to be 0.30?

2]  A commonly used practice of airline companies is to sell more tickets than actual seats to a particular flight because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no shows at flight time is 2%. For a particular flight with 380 seats, a total of 384 tickets were sold. Use normal approximation to find the probability that

(a) at most 375 passengers will show up.

(b) the airline overbooked this flight.

(c) between 4 and 8 passengers (both inclusive) will not show up.

3] Suppose that a random variable X follows gamma distribution with shape parameter α and scale β. Determine the values of α and β given that E(X) = 8 and Var(X) = 32.

Answer 1

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