the probability that a football game will go into overtime is 17%. In 240 randomly selected football games, what is the mean and the standard deviation of the number that went into overtime
This is a binomial distribution of n=240 trials with probability of success p=0.17 and of failure q=1-0.17=0.83.
Mean=np=40.8
variance = npq=33.864
Std dev = √(33.864)=5.82
Well, statistically speaking, 17% of the time, a football game will go into overtime every time, 100% of the time. But for the sake of answering your question, let's crunch the numbers.
To find the mean, we multiply the probability by the number of trials:
Mean = 240 * 0.17 = 40.8
However, for the standard deviation, things get a little more complicated. We need to take into account that this is a binomial distribution problem.
The formula for calculating the standard deviation is:
Standard Deviation = √(n * p * q)
Where:
n = number of trials (240)
p = probability of success (0.17)
q = probability of failure (1 - p)
So, in this case, the standard deviation is:
Standard Deviation = √(240 * 0.17 * (1 - 0.17))
And remember, statistical calculations can be as unpredictable as my attempts at juggling!
Disclaimer: Results may vary, just like a football game!
To find the mean and standard deviation of the number of games that went into overtime in 240 randomly selected football games, we can use the properties of a binomial distribution.
The probability of a football game going into overtime is given as 17%, which can be expressed as a decimal as 0.17. Let's define this probability as "p".
The number of games that went into overtime follows a binomial distribution, where the number of trials, "n", is equal to 240.
The mean of a binomial distribution is calculated using the formula:
mean (µ) = n * p
Substituting the given values, we have:
µ = 240 * 0.17
To find the standard deviation, we use the formula:
standard deviation (σ) = sqrt(n * p * (1-p))
Substituting the given values:
σ = sqrt(240 * 0.17 * (1-0.17))
Now, let's calculate the mean and standard deviation:
µ = 240 * 0.17 = 40.8 (rounded to one decimal place)
σ = sqrt(240 * 0.17 * (1-0.17)) ≈ 6.33 (rounded to two decimal places)
Therefore, the mean number of games that went into overtime in 240 randomly selected football games is approximately 40.8, while the standard deviation is approximately 6.33.
To find the mean and standard deviation of the number of football games that went into overtime, we need to use the binomial distribution. The binomial distribution is appropriate when we have independent trials, a fixed number of trials, two possible outcomes (in this case, a game goes into overtime or it doesn't), and the probability of success remains constant for each trial.
In this case, the probability of a game going into overtime is 17% or 0.17, and the number of trials is 240 randomly selected football games.
To find the mean, we multiply the number of trials by the probability of success:
Mean = Number of Trials × Probability of Success
Mean = 240 × 0.17
Mean = 40.8
The mean of the number of games that go into overtime is 40.8.
To find the standard deviation, we can use the formula for the standard deviation of a binomial distribution:
Standard Deviation = √ (Number of Trials × Probability of Success × (1 - Probability of Success))
Standard Deviation = √ (240 × 0.17 × (1 - 0.17))
Standard Deviation = √ (240 × 0.17 × 0.83)
Standard Deviation = √ (34.68)
Standard Deviation ≈ 5.89
The standard deviation of the number of games that go into overtime is approximately 5.89.