Question

What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?

a. 0.1

b. 0.4

c. 0.8

d. 1

e. Cannot be determined

Short answer

(b) The resultant probability is 0.4

Step-by-step solution

Given Information

The likelihood that a randomly selected subject completes more tasks than expected in a 5-minute period while listening to relaxing music.

Explanation for correct option 

Consider that the distribution of probability is

X	1	2	3	4
$\mathrm{P}\left(\mathrm{x}\right)$	0.20	0.40	0.30	0.10

The number of puzzles predicted to be completed in a 5-minute period while listening to smoothing music can be calculated as follows:

$$\begin{gathered} E\left(x\right)=\sum xp\left(x\right) \\ =1(0.2)+2(0.4)+3(0.3)+4(0.1) \\ =0.2+0.8+0.9+0.4 \\ =2.3 \end{gathered}$$

Thus, the likelihood that a randomly selected subject completes more problems than expected in a 5-minute period while listening to calming music can be computed as follows:

Explanation for incorrect option 

(a) The resultant probability will not be 0.1

(b) The resultant probability will not be 0.4

(c) The resultant probability will not be 0.8

(d) The resultant probability not be 1