Given that x is normally distributed random variable with a mean of 60 and a standard deviation of 10, find the following probabilities

standard-deviation
probabilities

#1

Given that x is normally distributed random variable with a mean of 60 and a standard deviation of 10, find the following probabilities.
a. P(x>60)
b. P(60<x<72)
c. P(57<x<83)
d. P(65<x<82)
e. P(38<x<78)
f. P(x<38)

Answer:

a. P(x>60) = P((X-mu)/s >(60-60)/10) = P(Z>0) = 0.5
b. P(60<x<72) = P(0<Z<(72-60)/10)= P(0<Z<1.2) = 0.3849
c. P(57<x<83) = P((57-60)/10 <Z< (83-60)/10) = P(-0.3<Z<2.3) = 0.6072
d. P(65<x<82) = P((65-60)/10 <Z< (82-60)/10) = P(0.5<Z<2.2) = 0.2946
e. P(38<x<78) = P((38-60)/10 <Z< (78-60)/10) = P(-2.2<Z<1.8) =0.9502
f. P(x<38) = P(Z<-2.2)=0.0139

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