This question is incomplete, the complete question is;
On the occasion of its 10-year anniversary, AJ Inc. sells lucky draw tickets. If the customers are interested in the lucky draw contest, then they have to purchase a ticket for $15. The gift could be worth $115, $215, $315, or nothing. The probability of each event is given below. What is the value of the standard deviation
Probability 0.35 0.26 0.21 0.18
Amount gained $100 $200 $300 -$15
Option;
a) $11,143
b) $106
c) $10,200
d) $147
Answer:
the standard deviation is 106
Option b) $106 is the correct Answer
Step-by-step explanation:
Given the data in the question;
let the random variable be x
x = amount gained by customers in a lucky draw contest
so
Variance (x) = [∑(x² × P(x))] - [(∑(x × P(x))²]
so
x x² p(x) x.p(x) x².p(x)
$100 10,000 0.35 35 3,500
$200 40,000 0.26 52 10,400
$300 90,000 0.21 63 18,900
-$15 225 0.18 -2.7 40.5
TOTAL 147.3 32,840.5
Variance (x) = [∑(x² × P(x))] - [(∑(x × P(x))²]
we substitute;
Variance (x) = 32,840.5 - (147.3)²
Variance (x) = 32,840.5 - 21,697.29
Variance (x) = 11,143.21
Now Standard Deviation = √variance
so, S.D = √11,143.21
S.D = 105.56 ≈ 106
Therefore, the standard deviation is 106
Option b) $106 is the correct Answer
