The probability that a football game will go into overtime is 18%. In 140 randomly selected football games, what is the mean and the standard deviation of the number that went into overtime?
To find the mean and standard deviation of the number of football games that went into overtime in 140 randomly selected games, we can use the properties of the binomial distribution.
The binomial distribution is used to model situations where there are two possible outcomes (success or failure) and a fixed number of independent trials, each with the same probability of success.
In this case, the probability of a football game going into overtime is 18%, which is equivalent to a success, while the probability of a game not going into overtime (ending in the usual time) is 1 - 18% = 82%, which is the failure.
The mean (μ) and standard deviation (σ) of a binomial distribution can be calculated using the following formulas:
μ = n * p
σ = √(n * p * q)
Where:
- n is the number of trials (in this case, 140 football games)
- p is the probability of success (in this case, 18% or 0.18)
- q is the probability of failure (in this case, 82% or 0.82)
Let's calculate the mean and standard deviation:
μ = 140 * 0.18 = 25.2
σ = √(140 * 0.18 * 0.82) ≈ 3.56
Therefore, the mean number of football games that went into overtime in 140 randomly selected games is approximately 25.2, and the standard deviation is approximately 3.56.