Question

thirty percent of consumers prefer to purchase electronics online. you randomly select 8 consumers. find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five.
(a) find the probability that the number that prefer to purchase electronics online is exactly five.
p(5) = 0.047
(round to three decimal places as needed.)
(b) find the probability that the number that prefer to purchase electronics online is more than five.
p(x > 5) = 0.011
(round to three decimal places as needed.)
(c) find the probability that the number that prefer to purchase electronics online is at most five.
p(x ≤ 5) =
(round to three decimal places as needed.)

Explanation:

Step1: Understand the complement rule

The probability that \( x \leq 5 \) is the complement of \( x > 5 \). So, \( P(x \leq 5)=1 - P(x > 5) \).

Step2: Substitute the known value

We know \( P(x > 5) = 0.011 \). So, \( P(x \leq 5)=1 - 0.011 \).

Step3: Calculate the result

\( 1 - 0.011 = 0.989 \).

Answer:

\( 0.989 \)