answer to three friends each create 4 bags of starter bread dough. after ten days, each of those four bags is then divided into
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Answer:
a) The likelihood that none of the sampled employees are from the Hawaii plant is 1.74%.
b) The chance that exactly 1 employee from the sample is found working in the Hawaii plant is 8.70%.
c) There is an 89.56% chance that 2 or more employees in the sample are from the Hawaii plant.
d) The probability that 9 employees from the sample are working at the Texas plant is 8.70%.
Step-by-step explanation:
Each employee has two potential employment locations: either Texas or Hawaii. Thus, the binomial probability distribution can be utilized to solve this scenario.
Binomial probability distribution
This distribution defines the probability of achieving exactly x successes in n trials where there are only two outcomes.
Here, denotes the number of ways to choose x objects from a set of n, represented by the subsequent formula.
And p is the probability of success occurring.
In this context, we know:
The sample comprises 10 employees, therefore .
a. Calculate the probability that none of the sampled employees are from the Hawaii plant (to 4 decimals)?
Given that 20 out of 60 employees are based in Hawaii:
We aim to find P(X = 0).
Thus, the likelihood that none in the sample are from Hawaii stands at 1.74%.
b. Calculate the probability that 1 employee from the sample is from the Hawaii plant?
This is represented as P(X = 1).
Therefore, there is an 8.70% possibility that 1 employee in the sample comes from Hawaii.
c. Calculate the probability that 2 or more employees in the sample are from the Hawaii plant?
We can observe two scenarios: either fewer than 2 employees are from Hawaii or 2 and beyond. The combined probabilities equal decimal 1. So:
We seek to find .
From problems a and b, we possess values for both probabilities.
Accordingly, the chance that 2 or more employees in this sample operate at the Hawaii plant is 89.56%.
d. Calculate the likelihood that 9 employees in the sample are working at the Texas plant?
This corresponds to the probability found in part b for 1 employee working in Hawaii.
Consequently, there is an 8.70% chance that 9 employees belong to the Texas plant.