Question

In: Statistics and Probability

The speed limit of a road is 65 miles per hour. The speed of a car...

The speed limit of a road is 65 miles per hour. The speed of a car on the highway follows a normal distribution with a mean of 70 and standard deviation of 5. What percent of the distribution breaks the speed limit?

The speed limit of a road is 65 miles per hour. The speed of a car on the highway follows a normal distribution with a mean of 70 and standard deviation of 5. A police officer will only react to speeding if the person is going 3 standard deviations above the average (z = 3). What is the speed at which he will react?

Expert Solution

Solution:

Given: The speed of a car on the highway follows a normal distribution with a mean of 70 and standard deviation of 5.

The speed limit of a road is 65 miles per hour.

Part a) What percent of the distribution breaks the speed limit?

That is find:

P( X> 65) =..........?

Find z score for x = 65

Look in z table for z = -1.0 and 0.00 and find corresponding area.

P( Z< -1.00 ) = 0.1587

thus

Thus 84.13% of the distribution breaks the speed limit.

Part b) A police officer will only react to speeding if the person is going 3 standard deviations above the average (z = 3).

What is the speed at which he will react?

Use following formula to find x value:

miles per hour.

The speed at which a police officer will react is 85 miles per hour.

orchestra answered 1 year ago

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