Given a random variable having the normal distribution with the mean = 16.2 and

Question

Given a random variable having the normal distribution with the mean = 16.2 and the standard deviation = 1.5625, find the probabilities that it will take on a value A) greater than 16.8 B) less than 14.9 C) Between 13.6 and 18.8 D) between 16.5 and 16.7 Given a random variable having the normal distribution with the mean = 16.2 and the standard deviation = 1.5625, find the probabilities that it will take on a value A) greater than 16.8 B) less than 14.9 C) Between 13.6 and 18.8 D) between 16.5 and 16.7 A) greater than 16.8 B) less than 14.9 C) Between 13.6 and 18.8 D) between 16.5 and 16.7

Explanation / Answer

Data:

mean : 16.2

standard deviation: 1.5625

a) P=> 16.8

x=16.8 z= (16.8-16.2)/(1.5625) =0.384 so the probability P=>1.68 is = 0.3520

b) P=< 16.8

x=14.9 z= (14.9-16.2)/(1.5625) =-0.832 so the probability P=>14.9 is = 0.2033

b) 13.6<= P=> 18.8

x=13.6 z= (13.6-16.2)/(1.5625) =-1.664 so the probability P=>13.6 is = 0.0485

x=18.8 z= (18.8-16.2)/(1.5625) =1.66 so the probability P=>14.9 is = 0.0485

so the probability is 0.5-0.0485 =0.4515*2 =0.903

d) 16.5<= P=> 16.7

x=16.5 z= (16.5-16.2)/(1.5625) =0.192so the probability P=>16.5is = 0.4247

x=16.7 z= (16.7-16.2)/(1.5625) =0.32 so the probability P=>16.7 is = 0.3745

so the probability is 0.4247-0.3745 =0.052

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