The probability of a sample of 144 producing a mean of 50 or larger if the population has a mean of 49 and a standard deviation of 5 is approximately 0.0082 or 0.82%.
To solve this problem, we can use the central limit theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
First, we need to calculate the standard error of the mean (SEM) using the formula: