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MrRa [10]
3 years ago
6

Sixty-five percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly sele

ct 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?
Mathematics
1 answer:
Serhud [2]3 years ago
3 0

Answer:

The outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.

Step-by-step explanation:

The outcomes provided are:

(A) 0, 1, 2, 6, 7, 8

(B) 0, 1, 2, 7, 8

(C) 0, 1, 7, 8

(D) 0, 1, 2, 8

Solution:

The random variable <em>X</em> can be defined as the number of employees who judge their co-workers by cleanliness.

The probability of <em>X</em> is:

P (X) = 0.65

The number of employees selected is:

<em>n</em> = 8

An unusual outcome, in probability theory, has a probability of occurrence less than or equal to 0.05.

Since outcomes 0 and 1 are contained in all the options, we will check for <em>X</em> = 2.

Compute the value of P (X = 2) as follows:

P(X=2)={8\choose 2}(0.65)^{2}(0.35)^{8-2}

                =28\times 0.4225\times 0.001838265625\\=0.02175\\\approx 0.022

So <em>X</em> = 2 is unusual.

Similarly check for X = 6, 7 and 8.

P (X = 6) = 0.2587 > 0.05

X = 6 not unusual

P (X = 7) = 0.1373 > 0.05

X = 7 not unusual

P (X = 8) = 0.0319

X = 8 is unusual.

Thus, the outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.

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