An analog signal received at a detector (ASD) has strength which has a normal di

Question

An analog signal received at a detector (ASD) has strength which has a normal distribution with = 95 microvolts and a standard deviation of  =5.7 microvolts. Suppose that we measure 456 independent analog signals at the detector. Let x be the mean strength and X be the random variable representing the mean strength and let Xtot be the random variable representing the sum of the strengths of the 456 received signals.

c) About how many of the 456 signals have strengths above 101 microvolts? (nearest integer)  

d) About how many of the 456 signals have strengths between 90 and 100 microvolts?(nearest integer)  

e) What is the standard deviation of the distribution of X?  

f) What is the standard deviation of the distribution of Xtot?   

Explanation / Answer

c)here P(X>101) =P(Z>(101-95)/5.7)=P(Z>1.0526)=1-P(Z<1.0526)=1-0.8537=0.1463

therefore number haveing strenegth above 101 microvolts=0.1463*456=66.69 ~ 67

d)P(90<X<100)=P(-0.8772<Z<0.8772)=0.8098-0.1902=0.6196

therefore number haveing strenegth between 90 and 100 microvolts=0.6196*456=~283

e)  standard deviation of the distribution of X =5.7/(456)1/2 =0.2669

f)tandard deviation of the distribution of Xtot =5.7*(456)1/2 =121.7187

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