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 4.0 million.
To find the probability that the mean salary of the 100 players exceeded R 4.0 million, we first need to calculate the z-score for this value using the formula:
z = (X - μ) / (σ / √n)
Where:
X = R 4.0 million
μ = R 3.26 million
σ = R 1.2 million
n = 100
z = (4.0 - 3.26) / (1.2 / √100)
z = 0.74 / 0.12
z = 6.17
Now, we will look up the z-score of 6.17 in the standard normal distribution table to find the probability.
Since the z-score is very high, the probability of the mean salary of the 100 players exceeding R 4.0 million will be very close to 1 (or 100%). This means that it is almost certain that the mean salary of the 100 players will exceed R 4.0 million.