3.12 Speeding on the I-5, Part I: The distribution of...

3.12 Speeding on the I-5, Part I: The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.1 miles/hour and a standard deviation of 4.7 miles/hour. Use this information to answer the following questions. Round your answers to 2 decimal places. a) What percent of passenger vehicles travel slower than 80 miles/hour? b) What percent of passenger vehicles travel between 60 and 80 miles/hour? c) How fast do the fastest 5.5% of passenger vehicles travel? d) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5.

Transcript

00:01 There is given a normal distribution here, and the mean value was given.

00:05 So the mean, which is denoted by minute, this is 72 .1.

00:10 And what about for the standard deviation, this is denoted by sigma.

00:15 That was given as 4 .7 mile per hour.

00:20 And let me just define the random variable here, so i can define the random variable x, which is normally distributed, the mean value, and the standard deviation.

00:31 Okay, let's take a look at the part a.

00:34 What percent of passenger travel is slower than 80 miles? so that means we have to find random variable x, which is less than 80.

00:43 So i'm going to use the normal cdf function here.

00:46 The lower boundary, there is no in a lower boundary.

00:49 I'm going to put negative 1 , and the upper boundary is 80, the mean value, and the standard division.

00:56 Let's get the answer.

00:57 Press second and variance.

00:59 The second option i'm going to select.

01:00 This is negative 1 second e 99 and the upper boundary is 80 and the mean value is 72 .1 and the standard division this is 4 .7 so we will get the probability which is 0 .95 and 36 but the question is being asked the percentage form so i'm going to multiply this by a hundred which will 95 .36 percent and what about for part b so in this case the random variable x that is between 60 and 80 right again i'm going to use the normal cdf function so in this case the lower boundary is 60 upper boundary is 80 the mean value is 72 .1 and the standard division let's get the answer again second variance the second option so the lower boundary 60 the upper boundary is 80 the mean value is 72 .1 and the standard division this is 4 .7 so the answer would be this is 0 .94 and let's say 86 multiplied by 100 this is 94 .86%.

02:10 And let's take a look at the c here.

02:13 So how fast do the fastest 5 .5 passengers vehicles travel.

02:20 So that means if i just graph the normal distribution here.

02:25 So let's say we have, let's just use another graph here, let's say this one.

02:32 So let's say we have the x1 value here and let's say this region is the fastest 5 .5%.

02:40 This is 0 .055%...