John Beale of Stanford, California, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a two-month period. These are 100 representative readings.) a. How many standard deviations from the mean would a car going under the speed limit be? b. Which would be more unusual, a car traveling 34 mph or one going 10 mph?

Question

16-09-2022
Mathematics

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John Beale of Stanford, California, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a two-month period. These are 100 representative readings.) a. How many standard deviations from the mean would a car going under the speed limit be? b. Which would be more unusual, a car traveling 34 mph or one going 10 mph?

Answer :

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ogorwyne ogorwyne · Answer 1 · 2022-09-20T15:29:08-04:00

How many standard deviations from the mean would a car going under the speed limit be -1.0787

Which would be more unusual: a car traveling 10 mph

Given data:

At speed limit of 20 mph mean of 100 readings was 23.84 mph

and a standard deviation of 3.56 mph

The speed limit read 20 mph

How to find the standard deviations from the mean that the car going under the speed limit

Assuming the car going under the speed limit of 20 mph be y

such that

20 = 23.84 + y * 356

356y = 20 - 23.84

y = ( 20 - 23.84 ) / 356

y = -1.0787

How to find which is more unusual

A car traveling 34 mph: using y same as number of deviations from the mean

34 = 23.84 + 3.56y

y = ( 34 - 23.84 ) / 3.56

y = 2.8539

Meaning the car travelling at 34 mph is 2.8539 standard deviations above the mean

A car traveling 10 mph: using y same as number of deviations from the mean

10 = 23.84 + 3.56y

y = ( 10 - 23.84 ) / 3.56

y = -3.8876

Meaning the car travelling at 10 mph is 3.8876 standard deviations below the mean

From the the rule that 99.7% of the observations lie with in ±3 standard. The speed of 10 mph is outside these limits but 34 mph is within the limits. Hence we say that the car travelling 10 mph is more unusual

Read more on standard deviation here: https://brainly.com/question/12402189

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