Question

please explain this soultion clearly as i am confused

Problem 7 (10 marks) 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 12 pounds and a standard deviation of 5 pounds. a) What proportion of the dieters lost more than 10 pounds? (3 marks) b) What proportion of the dieters gained weight? (4 marks) c) What is the cut-off for the top 1% weight loss? (3 marks)

Answer 1

Let- weight loss is random variable x. XNN (12,52) also know that it x n N (4,02) X-M N(o,) we then z = @ P(x>10) = P(X512 310512) = P(Z > -0.4) from zorable calculator. PCX310) =0.65542 (6 To gain weight the random variable must be less than o. so PCXco) PC SP < 0-12) = P(Z <-2.4) from 2-table calculator. Placo) = 0.00 8197 P(x > 20.01 ) = 0.01 P(x-12 20.07-12 J =0.01 5 P(Z > 20.01 - 12) = 0.01 5 from 2-table calculator. the Z-score is 2.326 No.01-12 2 2.326 xo.01 = 23.63