Question

1. suppose that computer literacy among people ages 40 and older is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that are computer literate. is it unusual to find four computer literates among four randomly selected people? a) yes

0 1 2 3 4
p(x) 0.16 0.25 0.36 0.15 0.08
b) no

Explanation:

Step1: Recall the criteria for a probability distribution

A probability distribution must satisfy two conditions: 1. \(0\leq P(x)\leq1\) for all \(x\), and 2. \(\sum_{x}P(x) = 1\).

Step2: Check the sum of probabilities

\(\sum_{x = 0}^{4}P(x)=0.16 + 0.25+0.36 + 0.15+0.08\)
\[

$$\begin{align*} &0.16+0.25 + 0.36+0.15+0.08\\ =&(0.16 + 0.25)+0.36+(0.15 + 0.08)\\ =&0.41+0.36 + 0.23\\ =&0.77+0.23\\ =&1 \end{align*}$$

\]
Also, \(0\leq0.16\leq1\), \(0\leq0.25\leq1\), \(0\leq0.36\leq1\), \(0\leq0.15\leq1\) and \(0\leq0.08\leq1\). So it is a valid probability - distribution.

Step3: Check for unusualness

An event is considered unusual if its probability is less than or equal to \(0.05\). The probability of having four computer - literates \(P(x = 4)=0.08>0.05\). So it is not unusual.

Answer:

B. No