Major league baseball salaries averaged R3.26 million with a standard deviation of R 1.2 million in a recent year. Suppose a sample of 100 major league players was taken.
Find the probability that the mean salary of the 100 players exceeded R 3.5 million.
To find the probability that the mean salary of the 100 players exceeded R 3.5 million, we need to calculate the z-score of this value and then look up the probability in the standard normal distribution table.
First, calculate the z-score:
z = (X - μ) / (σ / sqrt(n))
z = (3.5 - 3.26) / (1.2 / sqrt(100))
z = 0.24 / 0.12
z = 2
Now, look up the probability of z = 2 in the standard normal distribution table. The probability of z = 2 is approximately 0.9772.
Therefore, the probability that the mean salary of the 100 players exceeded R 3.5 million is 0.9772, or 97.72%.