Question

The length of unemployment for individuals during a pandemic has mean of 32 weeks and standard deviation is 2.6 weeks. Assume that the length of unemployment has a Normal distribution. You select a random sample of 324 unemployed individuals and record how long they have been unemployed. Find the probability that the length of unemployment of a single randomly selected individual is greater than 31.9. 324 is greater Find the probability that the average length of unemployment for the sample of size n = than 31.9.

Answer 1

Griven Mean(M) = 32 SD ( 0-2.6 n=324 Noomelly distributed single individual: 0 P(x731.9) for method to find P(x231.9) we Z-slore use z = x-u - 31.9-32 2.6 -0.04 2= -0.04 P(x>31.9) = P(z>-0.04) And P(27-0.04) = o.s 16 (from Standard Normal Jablk P(X>31.9) = 0.516 * Aug D P(x2319) for Sample size n=324 - Here z= xom r/55 31.9-32 2.615324 = -0.6923 z - -0.6923 And Plz>-0.6923) = 0.7549 (from Standard norma P(x731-9) = 0.7549 * Ang