Question 980106: One knows that the years of experience of different supervisors in a company follow a normal distribution with a mean of 7,8 and a standard deviation of 1,5.
If you take a random sample of 16 supervisors: what is the probability that less than 20% of them have between 8 and 10 years of experience?"
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! mean is 7.8, sd is 1.5
z for 8= +0.2/1.5=0.133
z for 10=2.2/1.5 =1.466
The probability of falling in that range is 0.3758 for each one
want 0,1,2,3 since all are fewer than 20% of all
Probability none do is 1*(0.6242)^16=0.0005
of 1:= 15*(0.3758)(0.6242)^15= 0.0048
of 2= 15C2(0.3758^2)(0.6242)^14;= 0.0202
15C2=105
of 3: 15C3 (0.3758)^3(0.6242)^13= 0.0527
15C3=455
The probability is the sum or 0.0782. The expected value would be between 5 and 6
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