Answer to Question #146080 in Statistics and Probability for Ann

Question

Given that the prices of sardines sold at the market is normally distributed with a mean price of Ph15.00 per can and a standard deviation of Ph1.20. Give a detailed description of the population of prices of the cans of sardines with emphasis on the bottom and top 16 % on one hand and the bottom and top 5% on the other while picturing out the greater and the super majority.

Answer 1

p - price

P - probability

Z=(p-15)/1.2

p = Z*1.2+15

bottom 16%; P(x<Z) = 0.16; Z = -0.994; p<13.81

top 16%; P(x>Z) = 0.16; Z = 0.994; p>16.19

bottom 5%; P(x<Z) = 0.05; Z = -1.645; p<13.03

top 5%; P(x>Z) = 0.05; Z = 1.645; p>16.97

greater (>50%); P(-Z<x<Z)=0.5; Z=0.674; 14.19<p<15.81

super majority (>2/3); P(-Z<x<Z)=0.667; Z=0.968; 13.84<p<16.16

Greater:

Super majority: