Assume that a random variable is normally distributed with a mean of 1, 200 and

Question

Assume that a random variable is normally distributed with a mean of 1, 200 and a variance of 373. Complete parts a through c below. a. What is the probability that a randomly selected value will be greater than 1, 224? The probability is (Round to four decimal places as needed.) b. What is the probability that a randomly selected value will be less than 1, 125? The probability is (Round to four decimal places as needed.) c. What is the probability that a randomly selected value will be either less than 1, 142 or greater than 1, 257? The probability is (Round to four decimal places as needed.)

Explanation / Answer

Mean is given as 1200 and standard deviation is sqrt(373)= 19.31

A. P(x>1224)= P(z>(1224-1200)/19.31)=P(z>1.24) or 1-P(z<1.24) . From normal distribution table we get 1-0.8944 or 0.1056

B. P(x<1125)= P(z<(1125-2000)/19.31)=P(z<-3.89) or 1-P(z<3.89). From normal distribution table we get 1-1 or 0

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