A lawyer commutes daily from his suburban home to his...

A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 2424 minutes, with a standard deviation of 4.14.1 minutes. Assume the distribution of trip times to be normally distributed

Transcript

00:01 In this video, we are going to look at to calculate the 95th percentile to calculate the 95th percentile of the lawyer's trip time, of the lawyer's trip time.

00:26 All right? so it has been given in our question that the average time for one trip is going to be 24 minutes.

00:37 Therefore i can say that the value of the mean mu is given as 24 minx all right and further the standard deviation which is denoted by sigma the value the standard division is 3 .8 minutes the value of the standard division is nothing but 3 .8 minutes now this distribution of the trip time is basically following the normal distribution okay so first of all let us assume our random variable x and this random variable x denotes the time for one -way trip time for one way okay so this is the time for the one -way therefore i can say that the x is following the normal distribution with the value of the mean to be equals to 24 all right and the value this variance is going to be equals to 3 .8 is here 3 .8 is basically the standard deviation and the square of the standard deviation is our variance okay now here we are going to look at to calculate the 95th percentile and for this let us suppose the k denotes our 95th percentile k denotes 95th percentile so in this case we can say that the probability that the capital x which is basically the time for a one vector is going to be less than or equals to k and this value is going to be basically 0 .95 okay now i'm going to subtract the value of the mean from both side and divide it further by standard deviation so it won't have any effect on either of these two so it will be the probability that x minus the value of the mean is 24 over i'm going to divide it by standard division which is 3 .8 and this value is smaller than or equals to k minus 24 over 3 .8 and this will give us the value of 0 .95 okay so this is the value now moving further if i ask you what this value is, so this is basically x minus mu over sigma and this x minus me over sigma is nothing but z.

02:52 So i can say that this is z to be less than or equals to k minus 24 over 3 .8 and that should give us the value of 9 .95...

Question

A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 2424 minutes, with a standard deviation of 4.14.1 minutes. Assume the distribution of trip times to be normally distributed

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