One of the variables measured is the severity of a driver\'s head injury when th

Question

One of the variables measured is the severity of a driver's head injury when the car is in a head on collision with a fixed barrier while traveling at 35 MPH. The more points assigned to the head injury rating, the more severe the injury. answer the following questions if one of the crash tested cars is randomly selected from the data and the driver's head injury rating is observed. A. Find the probability that the rating will fall between 500 and 700 points. B .Find the probability that the rating will fall between 400 and 500 points. c. Find the probability that the rating will be less than 850 points. d. Find the probability that the rating will exceed 1,000 points. e. What rating will only 10% of the crash-tested cars exceed?

Explanation / Answer

Mean and standard deviation cannot be calculated as the data is missing.

So, I'm assigning mean to 'm' and standard deviation as 's'.

a) Find the probability that the rating will fall between 500 and 700 points.

= P(500<X<700) = P ((500-m)/s < Z < (700-m)/s)

P(Z < (700-m)/s) - P ((500-m)/s)

If you have m & s values, plug in the values to this equation and calculate the probability.

b) Find the probability that the rating will fall between 400 and 500 points.

= P(400<X<500) = P ((400-m)/s < Z < (500-m)/s)

P(Z < (500-m)/s) - P ((400-m)/s)

If you have m & s values, plug in the values to this equation and calculate the probability.

c) Find the probability that the rating is less than 850 points.

= P(X<850) = P ( Z < (850-m)/s)

If you have m & s values, plug in the values to this equation and calculate the probability.

d) Find the probability that the rating is more than 850 points.

= P(X> 1000) = P ( Z > (1000-m)/s)

If you have m & s values, plug in the values to this equation and calculate the probability.

e)  What rating will only 10% of the crash-tested cars exceed

P(Z > z) =10%

1 - P(Z <= (X-m)/s)=0.1

so, (X-m)/s=1.2 (from standard normal tables)

So, X=1.2s+m

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