Answer to Question #230057 in Quantitative Methods for chisenga

Question

Sports shirts are frequently classified as S, M, L, XL for small, medium, large

and extra-large neck sizes. S fits a neck circumference of less than 37cm, M

fits between 37 and 40.5cm and L fits between 40.5cm and 44cm while XL fits

necks over 44cm in circumference. The neck circumference of adult males has

a normal distribution with µ = 40cm and σ = 2cm.

(i) If you wanted to define categories S, M, L, XL so that the categories con-

tained 20%, 30%, 30% and 20% respectively, of the total population of

adult males, what neck sizes must you assign to each of the categories?