The mean of a normal probability distribution is 400 pounds. The standard deviat

Question

The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. 13 a. What is the area between 415 pounds and the mean of 400 pounds? (Round your answer to 4 decimal places.) .25 points eBook Hint Ask References b. What is the area between the mean and 395 pounds? (Round your answer to 4 declmal places.) e What is the probability of selecting a value at random and discovering thet it has a value of less than 395 pounds? (Round your answer to 4 decimal places.) Prex 13 of 1611 Next > 26

Explanation / Answer

Mean is 400 and s is 10. z is given as (x-mean)/s

a) P(400<x<415)=P((400-400)/10<z<(415-400)/10)=P(0<z<1.5) or P(z<1.5)-P(z<0), from normal table we get 0.9332-0.5=0.4332

b) P(395<x<400)=P((395-400)/10<z<(400-400)/10)=P(-1.5<z<0)=P(z<0)-P(z<-1.5) or P(z<0)-(1-P(z<1.5))=0.5-(1-0.9332)=0.4332

c) P(x<395) =P(z<(395-400)/10)=P(z<-1.5) or 1-P(z<1.5)=1-0.9332=0.0668

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