Question

A population of values has a normal distribution with u = 146.6 and o = 66.3. You intend to draw a random sample of size n = 186. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is greater than 152.4. PIX > 152.4) = Find the probability that a sample of size n = 186 is randomly selected with a mean greater than 152.4. Plı > 152.4) =

Answer 1

let X be a Nomally distributed sandom variable, with mean u=146.6 o = 66-3. S9 n=186. Sample size I plx>152-4) =P(R-u 152.4-146-6 =P(2>0.09) 66.3 =1-(z<0.09) = 1-0.5359 = 0.4641 2. Plă, 152-4) P(x-u 1526-1466 66.3 15186 = P(Z=119) = 1-p(221:19) = 1-0.8830 = 0.117.