Morgan trucking company determined that on an annual basis the distance traveled per truck is normally distributed with a mean of 50 thousand miles and standard deviation of 12 thousand miles. 1)What the probability that a truck travels less than 34 thousand miles per year?2)What is the probability that a truck travels between 34 and 50 thousand miles per year?3)What is the probability that a truck travel more than 70 thousand miles per yea

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Asked Oct 10, 2019
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Morgan trucking company determined that on an annual basis the distance traveled per truck is normally distributed with a mean of 50 thousand miles and standard deviation of 12 thousand miles.
1)What the probability that a truck travels less than 34 thousand miles per year?
2)What is the probability that a truck travels between 34 and 50 thousand miles per year?
3)What is the probability that a truck travel more than 70 thousand miles per yea

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Expert Answer

Step 1

It is given that mean and standard deviation are 50 and 12, respectively.

Step 2

Let the variable X denotes the annual basis the distance travelled per truck.

a.

The probability that a truck travels less than 34 thousand miles per year is obtained as follows:

P(x<34) Px-50
12
34 50
12
= P(:<-1.33)
0.0918. Using standard normal table)
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P(x<34) Px-50 12 34 50 12 = P(:<-1.33) 0.0918. Using standard normal table)

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Step 3

b.

 

The probability that a truck travels between 34 and 50 thousand miles per year is obtained as follows:

...
34 50
50 50
х — 50
P(34 xs 50) P
12
12
12
P(-1.33 0)
P(s0)-P(-1.33)
0.5000 0.0918 (-.- Using standard normal table
= 0.4082
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Image Transcriptionclose

34 50 50 50 х — 50 P(34 xs 50) P 12 12 12 P(-1.33 0) P(s0)-P(-1.33) 0.5000 0.0918 (-.- Using standard normal table = 0.4082

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