Final answer:
The standard deviation for the number of wins in a lottery given a win probability of 172,639 in 664 plays is approximately 11.0625.
Step-by-step explanation:
To calculate the standard deviation for the number of wins in a lottery, we can use the binomial distribution model. Since the probability of winning the lottery stays constant for each time a person plays, the situation can be modeled as a binomial experiment.
The formula for the standard deviation (σ) of a binomial distribution is:
σ = √Npq
Where:
- N is the number of trials (times the lottery is played)
- p is the probability of winning
- q is the probability of losing (1-p)
The probability of winning is given as 172,639 in 664 plays, so:
p = 172,639 / 664 ≈ 0.2599 (rounded to four decimal places)
The probability of losing is:
q = 1 - p ≈ 1 - 0.2599 ≈ 0.7401
Now we can calculate the standard deviation:
σ = √(664 * 0.2599 * 0.7401)
σ = √(122.3821)
σ ≈ 11.0625 (rounded to four decimal places)
Therefore, the standard deviation for the number of wins is approximately 11.0625.
.