SOLUTION: Suppose a candy manufacturer claims that 20% of a particular candy it makes is orange. You purchase a package and find that the package has thirteen pieces in it. a. Find the mea

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose a candy manufacturer claims that 20% of a particular candy it makes is orange. You purchase a package and find that the package has thirteen pieces in it. a. Find the mea      Log On


   

Question 369917: Suppose a candy manufacturer claims that 20% of a particular candy it makes is orange. You purchase a package and find that the package has thirteen pieces in it. a. Find the mean and standard deviation for the number of orange candies in each package of thirteen.
b. Using the probability outcome, comment on whether it would be unusual to find no orange candies in your package of thirteen.
c.Using the values of the mean and standard deviation, comment on whether it would be unusual to find no orange candies in your package of thirteen.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a) P%28Orange%29=0.2
Let's look at the probabilities for 13 pieces.
P%280%29=+++1%2A%280.2%29%5E0%2A%280.8%29%5E13=0.054976
P%281%29=++13%2A%280.2%29%5E1%2A%280.8%29%5E13=0.178671
P%282%29=++78%2A%280.2%29%5E2%2A%280.8%29%5E13=0.268006
P%283%29=+286%2A%280.2%29%5E3%2A%280.8%29%5E13=0.245672
P%284%29=+715%2A%280.2%29%5E4%2A%280.8%29%5E13=0.153545
P%285%29=1287%2A%280.2%29%5E5%2A%280.8%29%5E13=0.069095
P%286%29=1716%2A%280.2%29%5E6%2A%280.8%29%5E13=0.023032
P%287%29=1716%2A%280.2%29%5E7%2A%280.8%29%5E13=0.005758
P%288%29=1287%2A%280.2%29%5E8%2A%280.8%29%5E13=0.00108
P%289%29=+715%2A%280.2%29%5E9%2A%280.8%29%5E13=0.00015
P%2810%29=286%2A%280.2%29%5E10%2A%280.8%29%5E13=0.000015
P%2811%29=+78%2A%280.2%29%5E11%2A%280.8%29%5E13=0.000001022
P%2812%29=+13%2A%280.2%29%5E12%2A%280.8%29%5E13=0.000000043
P%2813%29=++1%2A%280.2%29%5E13%2A%280.8%29%5E13=0.000000001
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mu=sum%28x%2AP%28x%29%2Ci=0%2C13%29
mu=2.6
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VAR=sum%28%28x-mu%29%5E2%2AP%28x%29%2Ci=0%2C13%29
VAR=2.08
sigma=sqrt%28VAR%29
sigma=1.44
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b) You'd expect to find between 2 and 3 orange candies in the package although zero is within 2 standard deviations of the mean, so it's not a very rare occasion.