Check the solution to "eighty percent of the employees at the General..."

College
Statistics and Probability
Upper level probability

mmayimutambi

Answered question

2022-05-26

eighty percent of the employees at the General mills' plant have their bimonthly wages sent by electronic transfer. suppose a researcher selects randomly seven employees and counts the number using direct deposit. What is the probability that all seven employees use direct deposit?

Answer & Explanation

Eliza Beth13

Skilled2023-05-17Added 130 answers

To solve the given problem, we'll use the concept of probability and assume that each employee's payment method is independent of others.
Given:
The probability of an employee using direct deposit is 80% or 0.8.
The researcher randomly selects seven employees.
To find the probability that all seven employees use direct deposit, we'll multiply the probability of each employee using direct deposit together since the events are independent.
Let's denote the event of an employee using direct deposit as D and not using direct deposit as N.
The probability of an employee using direct deposit is 0.8, and the probability of an employee not using direct deposit is 1 - 0.8 = 0.2.
Therefore, the probability of all seven employees using direct deposit can be calculated as follows:

P (D \cap D \cap D \cap D \cap D \cap D \cap D) = P (D)^{7}

Substituting the value of

P (D) = 0.8

, we have:

P (D \cap D \cap D \cap D \cap D \cap D \cap D) = {0.8}^{7}

Calculating this expression, we find:

P (D \cap D \cap D \cap D \cap D \cap D \cap D) \approx 0.2097

Therefore, the probability that all seven randomly selected employees use direct deposit is approximately 0.2097 or 20.97% (rounded to two decimal places).

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