Final answer:
To find the probability that more than eight patients arrive during a half-hour period at a maternity hospital, we can use the normal distribution. Using the average length of a stay and the standard deviation, we can calculate the z-score and find the probability using a z-table.
Correct option is A
Step-by-step explanation:
In this question, we are given the average length of a maternity hospital stay as 2.4 days with a standard deviation of 0.9 days. The question asks us to find the probability that more than eight patients arrive during a half-hour period.
To solve this problem, we can use the normal distribution. We know that the average length of a stay is 2.4 days and the standard deviation is 0.9 days, so we can calculate the z-score of 8 using the formula: z = (x - μ) / σ. Plugging in the values, we find that the z-score is approximately 7.11.
Using a z-table, we can find the probability that more than eight patients arrive during a half-hour period by subtracting the cumulative probability of z = 7.11 from 1. This gives us a probability of approximately 0.000000001. Therefore, it is extremely unlikely that more than eight patients will arrive during a half-hour period.