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Finding Binomial Probabilities In Exercises 1522, find the indicated probabilities. If
Chapter 4, Problem 15(choose chapter or problem)
Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four.
Questions & Answers
QUESTION:
Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four.
ANSWER:Step1 of 4:
From the given problem we have an experiment, In that 60% of U.S. adults trust national newspapers to present the news fairly and accurately. Also, we have n = 9.
Here our goal is:
a). We need to find the probability of getting exactly five U.S. adults trust national newspapers to present the news fairly and accurately.
b). We need to find the probability of getting at least six U.S. adults trust national newspapers to present the news fairly and accurately.
c). We need to find the probability of getting less than four U.S. adults trust national newspapers to present the news fairly and accurately.
Step2 of 4:
a).
Let us consider a random variable ‘x’ it presents the number of U.S. adults trust national newspapers to present the news fairly and accurately. Let us assume that ‘x’ follows the Binomial distribution with parameters ‘n and p’. That is:
\(\begin{aligned} X & \sim B(n, p) \\ X & \sim B(9,0.60) \end{aligned}\)
And