Answer :
Answer:
n = 144 bags
Step-by-step explanation:
Given:-
- English porcelain miniature figurines in total = 12
- 1 figurine is to be placed in a 100-bag box
Find:-
On the average, how many boxes of tea must be pur-chased by a customer to obtain a complete collection consisting of the 12 nautical figurines?
Solution:-
- We will denote a random variable (X) as the number of figurines in (n) number of bags purchased.
- The probability (p) of finding a figurine in a single bag is ( success ):
p = 1 / 12
- The random variable (X) can follow a binomial distribution with parameters n = number of bags purchased, and p = probability of selecting a bag with a figurine.
X ~ B ( n , 1/12 )
- The average number of bag "n" that need to be purchased to find all 12 figurines available:
E ( X ) = 12
n*p = 12
n = 12 / p
n = 12 / ( 1 / 12) = 12^2
n = 144 bags
- A total of average n = 144 bags need to be purchased to find all the 12 figurines.
A customer must purchase 37 boxes of tea to obtain a complete collection consisting of the 12 nautical figurines
The given parameters are:
[tex]n = 12[/tex] --- number of figurines
[tex]p = \frac 1{12}[/tex] ---the proportion of English porcelain miniature figurines
The number of bags to consist all 12 figurines is then calculated using:
[tex]E(x) = \sum np[/tex]
So, we have
[tex]E(x) = 12 \times (\frac{1}{12} +\frac{1}{11} + \frac{1}{10} +...........+1)[/tex]
[tex]E(x) = 12 \times 3.10[/tex]
Multiply
[tex]E(x) = 37.2[/tex]
Approximate
[tex]E(x) = 37[/tex]
Hence, a customer must purchase 37 bags
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