Question

New car crash tests.Refer to the National Highway TrafficSafety Administration (NHTSA) crash tests of new car models, Exercise 2.153 (p. 143). Recall that the NHTSA has developed a “star” scoring system, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. A summary of the driver-side star ratings for 98 cars is reproduced in the accompanying Minitab

Printout. Assume that one of the 98 cars is selected at random. State whether each of the following is true or false.

a.The probability that the car has a rating of two stars is 4.

b.The probability that the car has a rating of four or five stars is .7857.

c.The probability that the car has a rating of one star is 0.

d.The car has a better chance of having a two-star rating than of having a five-star rating.

Short answer

1. The solution is false.
2. The solution is true.
3. The solution is true
4. The solution is false.

Step-by-step solution

The probability that the car has a rating of two stars is 4.(a)

The solution is false because $\mathrm{P}\left(\text{2star}\right)=4.08\mathrm{\%}=0.048$.

Thus, the solution is false.

The probability that the car has a rating of four or five stars is .7857.(b)

The solution is true because

$\begin{array}{c}\mathrm{P}\left(4\text{\hspace{0.17em}star\hspace{0.17em}\hspace{0.17em}or\hspace{0.17em}\hspace{0.17em}}5\text{\hspace{0.17em}star}\right)=60.20\mathrm{\%}+18.37\mathrm{\%}\\ =6.020+1.837\\ =7.857\end{array}$

Accordingly, the solution is true.

The probability that the car has a rating of one star is 0.(c)

The solution is true, because the data of one star is not given, so the probability is 0.

Hence, the solution is true.

The car has a better chance of having a two-star rating than of having a five-star rating.(d)

The solution is false because the probability of two star rating is 0.048 and five star rating is 1.837.

Therefore, the solution is false.