The mean speed of a sample of vehicles along a stretch of...

The mean SPEED OF A SAMPLE OF VEHICLES ALONG A STRETCH OF HIGHWAY IS 55 MILES PER HOUR, WITH A STANDAR DEVIATION OF 5 MILES PER HOUR. U S E THE EMPIRICAL RULE. ESTIMATE THE PERCENT OF VEHICLES WHOSE SPEEDS ARE BETWEEN 39 MILES PER HOUR AND 69.5 MILES PER HOUR. (ASSUME THE DATA SET HAS A BELL-SHAPED DISTRIBUTION.) THE MEAN SPEED OF V EHICLES ALONG A STRETCH OF HIGHWAY IS 45 MILES PER HOUR WITH A STANDARD DEVIATION OF 5 MILES PER HOUR. YOU MEASURE THE SPEEDS OF THREE CARS TRAVELING ALONG THIS STRETCH OF HIGHWAY AS 65 MILES PER HOUR, 48 MILES PER HOUR, AND 58 MILES PER HOUR. FOR EMPIRICAL RULE x – ?s and x + ?s Where ? =1, 2, 3 The number of Standard Deviations

Transcript

00:01 All right, so in this question, we have two different parts.

00:04 So let's go ahead and start with the first part.

00:08 The first part of the question.

00:10 So we are given that the mean of the vehicles is 55 miles per hour, and the standard deviation is 5 miles per hour.

00:21 So we can use the empirical rule, and we know that about 68 % fall within one standard deviation.

00:31 According to this rule, and then 95 % fall within two standard deviations, two standard deviations, and 99 .7 fall within three standard deviations.

00:47 And this is just coming straight from the empirical rule.

00:52 So to estimate the percent of vehicles whose speeds are between 39, speed is between 39 and 69 .5, what we are going to have to do is find how many standard deviations away from the mean these two speeds are.

01:12 So the speed of 39 miles per hour is 16 miles per hour below the mean because the mean is 55.

01:22 So 55 minus 39 gives us 16.

01:28 So it is 16 divided by 16 divided by 5 standard deviations below the mean.

01:43 Okay, let's do the same thing, but for 69 .5.

01:50 So 55 minus 69 .5 gives us negative 14 .5.

01:57 So that means it's 14 .5 above the mean.

02:02 So 14 .5 divided by 5, and this gives us 2 .9 standard deviations above the mean.

02:13 So using the empirical rule, we can go ahead and estimate the percent of vehicles whose speeds are between 39 and 69 .5.

02:24 So that's going to be 0 .15 % plus, again, 0 .15%.

02:38 And this gives us 99 .4%.

02:50 Now, for the second part of this question, part two, we are given the mean speed, the mean speed of 45 miles per hour.

03:03 So it's different this time, 45 instead of 55...

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