Fresh features from the #1 AI-enhanced learning platform.Try it free
Fresh features from the #1 AI-enhanced learning platformCrush your year with the magic of personalized studying.Try it free
Question

# Based on the following table, which shows crashworthiness ratings for several categories of motor vehicles. In all of these exercises, take X as the crash-test rating of a small car, Y as the crash-test rating for a small SUV, and so on as shown in the table.$\begin{matrix} & \text{} & \text {} & \text{Overall Frontal Crash-Test Rating}\\ & \text{Number Tested} & \text{3 (Good)} & \text{2 (Acceptable)} & \text{1 (Marginal)} & \text{0 (Poor)}\\ \text{Small Cars X} & \text{16} & \text{1} & \text{11} & \text{2} & \text{2}\\ \text{Small SUVs Y} & \text{10} & \text{1} & \text{4} & \text{4} & \text{1}\\ \text{Medium SUVs Z} & \text{15} & \text{3} & \text{5} & \text{3} & \text{4}\\ \text{Passenger Vans U} & \text{13} & \text{3} & \text{0} & \text{3} & \text{7}\\ \text{Midsize Cars V} & \text{15} & \text{3} & \text{5} & \text{0} & \text{7}\\ \text{Large Cars W} & \text{19} & \text{9} & \text{5} & \text{3} & \text{2}\\ \end{matrix}$Compute the probability distributions and expected values of Z and V. Based on the results, which of the two types of vehicle performed better in frontal crashes?

Solution

Verified
Step 1
1 of 5

Given the frequency table for a random variable, we need to calculate its expected value.

Use the given table to calculate $P(Z=z)$ and $P(V=v)$, and

the expected value of both variables.

The vehicle type represented by a variable with the higher expected value has better performance.

## Recommended textbook solutions #### Finite Math and Applied Calculus

6th EditionISBN: 9781133607700 (2 more)Stefan Waner, Steven Costenoble
4,880 solutions #### Finite Mathematics and Calculus with Applications

9th EditionISBN: 9781256056706Margaret L. Lial, Nathan P. Ritchey, Raymond N. Greenwell
7,504 solutions #### Finite Mathematics for the Managerial Life and Social Sciences

12th EditionISBN: 9781337405782 (1 more)Tan, Soo
3,074 solutions #### Calculus

1st EditionISBN: 9781429215695Tan, Soo
8,315 solutions