Find the and variance of Y Find the probability that nobody

Find the and variance of Y. Find the probability that nobody of the 10 people has level higher than 1.5 mg/ml. Find the probability that at least 1 person has glycemia level higher than 1.5 mg/ml.

Solution

e)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    1.5      
u = mean =    1.15      
          
s = standard deviation =    0.3      
          
Thus,          
          
z = (x - u) / s =    1.166666667      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.166666667   ) =    0.121672505

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    10      
p = the probability of a success =    0.121672505      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.2732529 [ANSWER]

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f)

Thus, P(at least one) = 1 - P(0) =   0.7267471 [ANSWER]