Chapter 6.1, Problem 4E

(a)

To determine

To Calculate: $\text{P}\left(Y<20\right)$ and explain it

Answer to Problem 4E

  $\text{P}\left(Y<20\right)=0.32$

Explanation of Solution

Given:

Score	10	20	30	40	50
Probability	0.32	0.27	0.19	0.15	0.07

Calculation:

  $\begin{array}{c}\text{P}\left(Y<20\right)=\text{P}\left(Y=10\right)\\ =0.32\end{array}$

It is 0.32 probabilities that the score which is less than score of 20

(b)

To determine

To Calculate: the event for at most score 20 is in terms of Y and its probability

Answer to Problem 4E

  $Y\ge 20$

  $\text{P}\left(Y\ge 20\right)=0.68$

Explanation of Solution

Calculation:

  $\begin{array}{c}\text{P}\left(Y\ge 20\right)=\text{P}\left(Y=20\right)+\text{P}\left(Y=30\right)+\text{P}\left(Y=40\right)+\text{P}\left(Y=50\right)\\ =0.27+0.19+0.15+0.07\\ =0.68\end{array}$