A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a standard deviation of penalties per game. What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be penalties per game or more?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
It would help if you proofread your questions before you posted them. No values given.
Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the probability that the mean number of holding penalties in the sample of college games next week will be penalties per game or more, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.
Step 1: Calculate the z-score.
The z-score is calculated as (X - mean) / (standard deviation / sqrt(n)), where X is the value we want to find the probability for, mean is the mean number of holding penalties, standard deviation is the standard deviation of holding penalties, and n is the sample size.
In this case, we want to find the probability for penalties per game or more, so X is penalties per game.
Z = (X - mean) / (standard deviation / sqrt(n))
Z = ( - mean) / (standard deviation / sqrt(n))
Step 2: Look up the probability from the standard normal distribution.
Once we have the z-score, we can look up the probability using a standard normal distribution table or a statistical calculator.
The probability we want to find is the probability of getting a z-score greater than or equal to the calculated z-score.
P(Z ≥ z) = 1 - P(Z < z)
Step 3: Calculate the probability.
Using the information given, we can replace the values in the z-score formula and calculate the probability.
Z = ( - mean) / (standard deviation / sqrt(n))
P(Z ≥ z) = 1 - P(Z < z)
Finally, round the answer to at least three decimal places.
Please provide the values of the mean, standard deviation, and sample size (n) to complete the calculation.