a Find the mean resistance bFind the standard deviation of t

a. Find the mean resistance.

b.Find the standard deviation of the resistances.

Please show all work!

Solution

A)

Note that here,          
          
a = lower fence of the distribution =    95      
b = upper fence of the distribution =    103      
          
Thus, the mean, variance, and standard deviations are          
          
u = mean = (b + a)/2 =    99   [ANSWER]  

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B)

Also,

s^2 = variance = (b -a)^2 / 12 =    5.333333333      
s = standard deviation = sqrt(s^2) =    2.309401077 [ANSWER]

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c)      

          
Note that P(x>c) = P(c<x<b) = (b-c)/(b-a). Thus, as          
          
c = critical value =    100      
          
Then          
          
P(x<c) =    0.375   [ANSWER]

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d)

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 =    6      
p = the probability of a success =    0.375      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.257492065 [ANSWER]