Final answer:
To find the probability that the next 50 Sunday customers will spend an average of at least $40, we need to determine the probability distribution of the average spending per customer. Assuming a normal distribution, we can calculate the probability using the z-score formula.
Step-by-step explanation:
To find the probability that the next 50 Sunday customers will spend an average of at least $40, we first need to determine the probability distribution of the average spending per customer. Let's assume that the spending per customer follows a normal distribution with a mean of $35 and a standard deviation of $10.
To find the probability of the average spending being at least $40, we can use the z-score formula. The z-score is given by (X - μ) / (σ / sqrt(n)), where X is the desired average spending, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values, we get a z-score of (40 - 35) / (10 / sqrt(50)) = 2.23.
To find the corresponding probability, we can use a standard normal distribution table or a calculator. Looking up the z-score of 2.23 in the table, we find that the area under the curve to the right of this z-score is approximately 0.013. Therefore, the probability that the next 50 Sunday customers will spend an average of at least $40 is approximately 0.013.