### Normal distribution

Normal distribution

Question One Participation Question on Normal Distribution-1

Normal Distribution

In case of Normal distribution (problems from the textbook)

Find the probability for the standard normal random variable (Z) when (Z>1.46)

• Find the area under the standard normal probability distribution between the pairs of z-scores: Z=0 and Z=2.0

• Suppose x is a normally distributed random variable with mean of 11 and standard deviation of 2. Find the probability for p(10 = x = 12)

Question 2 Participation Question on Normal Distribution-2

Normal Distribution

Please answer the following from the textbook on NHTSA crash safety tests for new cars.

One of the variables saved in the CRASH file 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 miles per hour. The more points assigned to the head injury rating, the more severe the injury.

The head injury ratings can be shown to be approximately normally distributed with a mean of 605 points and a standard deviation of 185 points. 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 exceed1,000 points