Question

Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds.

a) What proportion of the dieters lost more than 12 pounds?

b) What proportion of the dieters gained weight?

c) What is the cut-off for the top 3% weight loss?

Answer 1

Xn N(M, 02) X~ N(10,5²) Meau r = 10 pounds standard deviation o=5 pound xor Z. Score a) Proportion of dieters lost more than 12 lbs is P(x>12) = P(Z > 12530) P(Z > ) = P(Z >0.4) 0.34458 Auswer b) Proportion of Dieters PCX<o) = P(Z < 0-0) = P(Z <-2) 0.02275 gained weight is Auswer ul 47% Top 3% loss OY c) Let P(Z>Z) = 0.03 (3%) P(Z >2) = POCZŁ0) - PlO<Z<z) weight PCO<Z«z) = P(0<z«o) - P(Z>2) = 0.5-0.03 Plac Z(z) 0.47 corresponds to 2 = 1.881 .. cut-off for top 3%, weight loss = M+ zo = 10+ 1.88115) 19.405 pounds Auswer