Question

31. The average pump price for regular gasoline across Canada ón à givěn day was SI1.03 pe litre, If gas prices are normally distributed with a standard deviation of S0.19, calculate the 15th and 85th percentile of Canadian gas prices.

Answer 1

Facts 1) If X, Z be the normal and standard normal distibuted random variables respectively. To find the probabilites forx we convert X to Z by using Z Where -mean(X) ơ-standard deviation(X) 2) P(Z 2 0)0.5 and P(Z s 0)-0.5 Let X be the random variable that represents price of a Canadian gas. Given that X follows normal distribution with mean() $1.05 and standard deviation (o) $0.19

a) Now we have to find the 15% percentile of Canadian gas prices. P(Z k) = 15% = 0.15 P(Z s 0) 0.5k must be negative 0.15 0.5 - PCO s Zs-k) From standard normal table see for what value of-k we can get P(0 Z <-k) = 0.35 →-k = 1.04 → k =-1.04 P(Z s-1.04) 0.15 P(Z * σ <-1.04 * 0.19)-0.15 P((Z * σ) + μ P(X s 0.8524)0.15 (-1.04 * 0.19) + 1.05)-0.15 15% percentile of Canadian gas prices-X-08524 85% percentile of Canadian gas prices 1-x(for 15% percentile) 1-0.8524 -1.2476