Question

the number of days ahead travellers purchase their airline tickets is exponentially distributed with average amount of time equal to 28 days. if there is 80 chance that a traveller will purchase the ticket fewer than d days in advance, then what is the value of d? write the answer to nearest digit integer.

Answer 1

The value of d where 80% of travelers purchase tickets fewer than d days in advance and the average time is 28 days, the exponential distribution CDF is used. Solving the equation 0.80 = 1 - e^(-(1/28)d), we find that d is approximately 39 days.

Step-by-step explanation:

The student's question deals with determining the value of d when the time to purchase an airline ticket is exponentially distributed, with an average amount of time equal to 28 days, and there is an 80% chance of a traveler purchasing the ticket fewer than d days in advance. To find the value of d, we use the cumulative distribution function (CDF) for the exponential distribution, which is 1 - e-λx, where λ is the rate parameter, λ = 1/mean, and x is the number of days.

Since the mean is 28, λ equals 1/28. We set the CDF to 0.80 and solve for d: 0.80 = 1 - e-(1/28)d. Solving for d yields that d ≈ 39 days. Therefore, travelers have an 80% chance of purchasing a ticket fewer than 39 days in advance.