Chapter 6, Problem T6.1SPT

To determine

To compute: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.

Answer to Problem T6.1SPT

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, is 0.40.

Explanation of Solution

Given:

The probability distribution is:

X	1	2	3	4
P(x)	0.20	0.40	0.30	0.10

Calculation:

The expected number of puzzles in the 5-minutes period while listening to smoothing music, can be calculate as:

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

Thus, 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, can be calculated as:

  $\begin{array}{c}P\left(X>2.3\right)=P\left(X=3\right)+P\left(X=4\right)\\ =0.30+0.10\\ =0.40\end{array}$

Thus, the correct option is “b”.