Question 1031227
Given information:
Expected value E is E = 221
Variance V is V = 33.15


We'll use the formulas
E = n*p
V = n*p*(1-p)
which are the formulas for the expected value and variance of a binomial distribution
n is the sample size
p is the probability of success
The ultimate goal is to find the value of n



Expected Value:
E = n*p
221 = n*p ... plug in the given expected value
n*p = 221



Variance:
V = n*p*(1-p)
V = 221*(1-p) ... plug in n*p = 221
33.15 = 221*(1-p) ... plug in the given variance



Now we solve for p
33.15 = 221*(1-p)
33.15 = 221-221p
33.15-221 = -221p
-187.85 = -221p
-221p = -187.85
p = -187.85/(-221)
p = 0.85



The probability of success is 0.85
This means the probability of picking one person who spent at least $10 is 0.85



Use p = 0.85 to find n



n*p = 221
n*0.85 = 221 ... plug in p = 0.85
n = 221/0.85
n = 260


So there are 260 people in the sample


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Final Answer: <font size=5 color = red>260</font>