On the eleventh day of Statistics, my teacher gave to me… eleven pipers piping. While these popular pipers are on tour piping, one piper is randomly selected to win tickets for his immediate family to the show. The breakdown of the number of tickets required follows: (2/11) of the pipers have one family member, (3/11) have two family members (4/11) have three family members, (1/11) has four family members, and the rest of the pipers have five family members. What is the mean number of tickets the popular piper-promoters must provide when the popular pipers perform proficiently? (In case you were wondering, Peter Piper is not a member of the tour group; he was to busy picking pecks of pickled peppers to perform piping proficiently with the popular pipers.)
In order to receive ANY credit, you must show correct formula, substitution and final answer VERTICALLY. If you need to use a symbol that does not exist on the keypad without going into Microsoft word, you may spell the symbol – such as MU.
mean*11families=2/11*1+3/11*2+4/11*3+1/11*4+5(1-2/11-3/11-4/11-1/11)
check that.
To find the mean number of tickets the popular piper-promoters must provide, we need to calculate the expected value.
The expected value is calculated by multiplying each possible outcome by its probability and summing them all up.
In this case, we have five possible outcomes: 1 family member, 2 family members, 3 family members, 4 family members, and 5 family members.
The probabilities for each outcome are given as (2/11), (3/11), (4/11), (1/11), and the remaining probability (1 - (2/11) - (3/11) - (4/11) - (1/11)).
Let's calculate the expected value step by step:
1. Begin by writing down the formula for expected value (mean):
E(X) = x1 * P(x1) + x2 * P(x2) + x3 * P(x3) + ...
2. Substitute the values for x1, x2, x3, etc. with the number of tickets required for each outcome (1, 2, 3, 4, 5).
3. Substitute the values for P(x1), P(x2), P(x3), etc. with the probabilities associated with each outcome.
4. Perform the multiplication for each outcome and its probability.
5. Sum up the results to get the expected value.
Let's calculate it step by step:
E(X) = (1 * (2/11)) + (2 * (3/11)) + (3 * (4/11)) + (4 * (1/11)) + (5 * (1 - (2/11) - (3/11) - (4/11) - (1/11)))
E(X) = (2/11) + (6/11) + (12/11) + (4/11) + (5 * (1 - (2/11) - (3/11) - (4/11) - (1/11)))
E(X) = 2/11 + 6/11 + 12/11 + 4/11 + 5/11
E(X) = 29/11
Therefore, the mean number of tickets the popular piper-promoters must provide when the popular pipers perform proficiently is 29/11.