Question

A random variable follows the normal probability distribution with a mean of 100 and a standard deviation of 10. Determine the probability for a randomly selected value from this population in parts a through d below. Click here to view.pa a. What is the probability that the value is less than 80? The probability that the value is less than 80 is (Round to four decimal places as needed.) b. What is the probability that the value is less than 70? The probability that the valueis less than 70 is (Round to four decimal places as needed.) c. What is the probability that the value is more than 105? The probability that the value is more than 105 is Round to four decimal places as needed.) d. What is the probability that the value is more than 95? The probability that the value is m ore than 95 is Round to four decimal places as needed.)

Answer 1

Given that, 100, 10 (a) The probability that the value is less than 80 is, 80-100 10 ( standard normal table) Φ(-2) 0.0228 Answer: 0.0228 (b) The probabilitythat the value is less than 70 is, -μ 70-μ 80-100 10 -3) = 0.0013 ( standard normal table)

Answer: 0.001:3 (c) The probability that the value is more than 105 is, P(x105)-1-P(x s 105) 105-100 = 1-0(0.5) ( standard normal table) 1-0.691 5 0.3085 Answer: 0.3085 (d) The probability that the value is more than 95 is,

P(X> 95) 1-P(Xs 95) (ZS95-100) :J-Φ(-0.5) ( standard normal table) 1-0.3085 0.6915 Answer: 0.6915