M&Ms Activity Tasks
1. Calculate
p
ˆ
numbers.
2. Write
p
ˆ
numbers in notebook.
3. Write each
p
ˆ
number on a separate Post-It Note.
4. Guess what
p
is.
5. Place Post-It Notes on the whiteboard.
Questions:
Assume
n
= 25 for calculations.
20% of the Milk Chocolate M&Ms in the world are orange so
p
= 0.20.
1. What is the area under the normal curve between 0.12 and 0.28?
normalcdf( 0.12, 0.28, 0.2, 0.08) = 0.6827 = 68.27%
Also, about 68% by the Empirical Rule.
2. What percent of sample packets have a proportion of orange M&Ms between 0.12
and 0.28?
normalcdf( 0.12, 0.28, 0.2, 0.08) = 0.6827 = 68.27%
Also, about 68% by the Empirical Rule.
3. What percent of packets have between 4% and 36% orange M&Ms?
normalcdf( 0.04, 0.36, 0.2, 0.08) = 0.9545 = 95.45%
Also, about 95% by the Empirical Rule.
4. What percent of packets have between 10% and 20% orange M&Ms?
normalcdf( 0.10, 0.20, 0.2, 0.08) = 0.3944 = 39.44%
5. What is the probability of opening a sample packet of M&Ms and have more than
50% of them be orange?
normalcdf( 0.50, 1E99, 0.2, 0.08) = 8.844E-5 = 0.00008844 = 0.008844%
6. What sample proportion of orange M&Ms do I need to have to be in the top 1%
of all sample packets?
InvNorm( 0.99, 0.2, 0.08) = 0.3861
Answer: The sample proportion must be 0.3861 or more!
In other words, at least 38.61% of the packet’s M&Ms must be orange
in order for the packet to be in the top 1% of all packets.