Respuesta :
Answer:
0,1, 2 and 3 employees judging their co-workers by cleanliness would be considered unusual.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
An outcome is considered unusual if it is more than 2.5 standard deviations from the mean.
Eighty-two percent of employees make judgements about their co-workers based on the cleanliness of their desk.
This means that [tex]p = 0.82[/tex]
You randomly select 7 employees and ask them if they judge co-workers based on this criterion.
This means that [tex]n = 7[/tex]
Mean:
[tex]E(X) = np = 7*0.82 = 5.74[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{7*0.82*0.18} = 1.02[/tex]
Two and a half standard deviations above the mean:
Will be higher than 7, so no possible values.
Two and a half standard deviations below the mean:
[tex]5.74 - 2.5*1.02 = 3.19[/tex]
So 0,1, 2 and 3 employees judging their co-workers by cleanliness would be considered unusual.
