Question

The partially completed table that follows shows the distribution of scores on the$2016$

AP® Statistics exam.

Suppose we randomly select a student who took this exam. What’s the probability that he

or she earned a score of at least$3$?

a.$0.249$

b.$0.361$

c.$0.390$

d.$0.466$

e.$0.610$

Short answer

The probability that he or she has earned a score of at least three is (e).$0.610$.

Step-by-step solution

Given Information

We are given the scores and the probability that one probability of score is missing, and we have to find out the probability that he or she has earned a score of at least three.

Explanation

In the given table, scores and probabilities are given but one probability is missing, as the sum of total probabilities is one.

So, we get $P\left(T\right)=1$where P(T) is the sum of all probability given

Putting the values we get,$0.235+0.155+0.249+0.217+x=1$

which states x$=0.144$,

So, now we have all probabilities.

Simplify

The probability of scoring at least three will be the sum of all probabilities greater than$3$including itself.

P($3$)$=0.249$, P($4$)$=0.217$,and P($5$)$=0.144$.

As, the P(T)$=P\left(3\right)+P\left(4\right)+P\left(5\right)$

On solving we get ,$P\left(T\right)=0.610$.

Hence, the probability of scoring at least three is$0.610$.