Final answer:
To calculate the probability of a sample mean greater than $2,000 in a normally distributed dataset, we must compute the standard error, find the z-score for $2,000, and then determine the probability from the standard normal distribution.
Step-by-step explanation:
The question asks about calculating the probability that the sample mean of the daily sales from a small retail store in Toronto will be more than $2,000 given that the sales are normally distributed with a mean of $2,050, and a standard deviation of $300. We can use the Central Limit Theorem since we have a large sample size (49 days), and we are dealing with a normal distribution. The sample mean has its own distribution, which is also normal, with a mean of $2,050 and a standard error (SE) calculated using the formula SE = σ/√n, where σ is the standard deviation and n is the sample size.
To find the probability that the sample mean is more than $2,000, we calculate the z-score for $2,000 using the formula: z = (X - μ)/SE, where X is $2,000, μ is the population mean of $2,050, and SE is the standard error just calculated. Then we look up this z-score in the standard normal distribution table or use a statistical software to find the corresponding probability.