It has been reported that the average hotel check in time...

It has been reported that the average hotel check-in time from arrival to the hotel is 12 minutes. Jack has just arrived at the hotel for check-in. Assuming check-in times follow a Normal distribution with a mean of 12 and a standard deviation of 2.0 minutes: (i) What is the probability that Jack's check-in time will be greater than 14 minutes? (ii) What is the probability that Jack's check-in time will be between 10 and 15 minutes? (iii) Determine, to two decimal places, the check-in time exceeded by 67% of guests in the hotel.

Transcript

00:01 We're looking at a normal distribution, so i'll start by drawing it.

00:04 These are the check -in times.

00:09 The mean, mu, is 12, standard deviation, sigma is 2.

00:15 And for part i, we want the probability that the check -in time is greater than 14 minutes.

00:22 So 14 is above the mean, i'll mark it on here.

00:25 We want greater than, so that's anything on the right.

00:28 So with the normal distribution, we don't use raw values, we turn them into z scores.

00:35 Z is x minus mu over sigma.

00:39 So the z score for 14 is 14 minus 12 over 2, 1.

00:45 That means it is one standard deviation above the mean.

00:49 Now to turn it into probability, you need either a z score table, a graphical calculator, or something like excel, anything with the normal functions baked into it.

00:57 And there are two such functions, you can use either one, standard and cumulative.

01:04 The standard function gives you the area between x and mu, your cutoff and the mean.

01:14 So this isn't quite what you want, but the area to the right of the mean is 0 .5, to the left the mean is 0 .5, because this is symmetric.

01:23 So if you take this away from 0 .5, you get your answer.

01:27 Cumulative gives you the area to the left.

01:31 So that's all of this.

01:33 Also not what you want, but if you take it away from one, total area under a probability curve, you have your answer.

01:40 I'll use standard, so whatever i get, taking away from 0 .5.

01:44 So i put in 1, i get 0 .3, 4 ,13.

01:51 So my answer is 0 .1587.

01:56 So that's part 1.

01:58 Part 2 is between 10 and 15.