Assume that a random variable is normally distributed with a mean of 1,300 and a

Question

Assume that a random variable is normally distributed with a mean of 1,300 and a variance of 256. Complete parts a through c below. a. What is the probability that a randomly selected value will be greater than 1,312? The probability is 2266 (Round to four decimal places as needed.) b. What is the probability that a randomly selected value will be less than 1,262? The probability is .0087 (Round to four decimal places as needed.) c. What is the probability that a randomly selected value will be either less than 1,277 or greater than 1,334? The probability is (Round to four decimal places as needed.)

Explanation / Answer

Q1 (a) P(X>1312)

= P(Z>(1312-1300)/Sqrt(256)

= 0.2266

b) P(X<1262)

= P(Z<(1262-1300)/Sqrt(256)

= 0.0087

c) P(X<1267)+ P(X>1334)

= 0.0921

Q2) a) P(X>5000)

= 0.1587

b) P(X<4000)

= 0.3341

c) P(1500<X<4200)

= 0.4432

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