Questions: 57% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.

57% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.

Transcript text: $57 \%$ of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.

Solution

Solution Steps

Step 1: Probability of Exactly 5 Adults

To find the probability that exactly 5 out of 10 U.S. adults have very little confidence in newspapers, we calculate $ P(5) $: \[ P(5) = 0.223 \]

Step 2: Probability of At Least 6 Adults

Next, we determine the probability that at least 6 U.S. adults have very little confidence in newspapers, which is calculated as: \[ P(X \geq 6) = 1 - P(X \leq 5) = 0.556 \]

Step 3: Probability of Less Than 4 Adults

Finally, we find the probability that less than 4 U.S. adults have very little confidence in newspapers: \[ P(X < 4) = 0.081 \]