Chapter 5.2, Problem 55E

To determine

To find: The correct option.

Answer to Problem 55E

The correct option is (e), 0.610.

Explanation of Solution

Given:

The probability distribution is:

Score	1	2	3	4	5
Probability	0.235	0.155	0.249	0.217	?

The provided options are:

(a) 249

(b) 0.361

(c) 0.390

(d) 0.466

(e) 0.610

Calculation:

Consider, the missing probability be x .

It is known that a distribution is said to be probability distribution, if its sum is equal to 1.

The value of x can be computed as:

  $\begin{array}{c}0.235+0.155+0.249+0.217+x=1\\ 0.856+x=1\\ x=0.144\end{array}$

Thus, the complete table of probability distribution is:

Score	1	2	3	4	5
Probability	0.235	0.155	0.249	0.217	0.144

Consider, Y be the random variable that shows the number of score earned.

The probability that a score of at least 3 has been earned by a randomly selected student can be calculated as:

  $\begin{array}{c}P\left(Y\ge 3\right)=P\left(Y=3\right)+P\left(Y=4\right)+P\left(Y=5\right)\\ =0.249+0.217+0.144\\ =0.610\end{array}$

Hence, the correct option is (e), 0.610.