Question

1. The manufacturers of m&m’s claim that 20% of the milk chocolate m&m candies are orange. If you take a random sample of 50 single serving size packages of m&m’s, what is the probability that the sample proportion of orange m&m’s is less than 9%. Use what you know about sampling distributions and the Empirical Rule to choose the best answer among those given below, and explain WHY you feel it is the best answer.

   1. 0.01(or 1%)

   2. 0.025 (or 2.5%)

   3. 0.05 (or 5%)

   4. 0.16 (or 16%)

Answer 1

Solution

Given that,

p = 0.20

1 - p = 1 - 0.20 = 0.80

n = 50

= p = 0.20

=  [p ( 1 - p ) / n] =   [(0.20 * 0.80) / 50 ] = 0.055

P( < 0.09)

= P[( - ) / < (0.09 - 0.20) / 0.055]

= P(z < -2.0)

Using Empirical rule

95% =     ± 2 *

=  50% - 95% / 2

= 50% - 47.5%

= 2.5% ( or 0.025 )