Question

NHTSA crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash tests of new car models, presented in Exercise. A summary of the driver–side star ratings for the 98 cars in the CRASH file is reproduced in the accompanying MINITAB printout. Assume that 1 of the 98 cars is selected at random, and let x equal the number of stars in the car’s driver–side star rating.

a. Use the information in the printout to find the probability distribution for x.

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b. Find P(x= 5).

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c. Find P(x≤ 2).

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d. Find μ = E(x) and interpret the result.

NHTSA crash tests. The National Highway Traffic Safety Administration (NHTSA) has developed a driver–side “star” scoring system for crash–testing new cars. Each crash–tested car is given a rating ranging from one star (*) to five stars (*****): the more stars in the rating, the better is the level of crash protection in a head–on collision. Suppose that a car is selected and its driverside star rating is determined. Let x equal the number of stars in the rating. Is x a discrete or continuous random variable?

Answer 1

(a)

From the known Minitab output, the obtained probability distribution is,

	Count
2	4
3	17
4	59
5	18
N	98

(b)

From the part (a), the required probability is,

(c)

From the part (a), the required probability is,

(d)

The expected value of X is,

Therefore, the expected value is 3.9286.