Question

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

Given,  $\mu =12, \sigma = 5$

a) Proportion of dieters lost more than 10 pounds=P(x>10)

1 - P(x<10)

= 1 - P(z<(10-12)/5)

= 1 - P(z< -0.4)

= 1 - 0.34458

= 0.65542

b) Proportion of dieters gained weight=P(x<0)

= P(z < (0-12)/5)

= P(z < -2.4)

= 0.0081975

c) Cutoff for top 1% weight loss is

= 0/0 - )

where z=2.33 (calculated by finding 1% that is 1-0.01=0.99 value in z table)

So, x=2.33*5 + 12

x= 23.65