Question 5(b) involves solving a problem related to the normal distribution and probabilities involving completion time of a table. Let's go step by step.

Problem Breakdown:

Given that the average time to complete a table is 10 minutes with a standard deviation of 2 minutes, we need to find:

1. The probability that a nurse has just started the task and will complete it within the next 8 to 10 minutes.

This can be solved using the normal distribution properties.

Solution Steps:

1. Define the Normal Distribution: The completion time $T$ follows a normal distribution with: $T \sim N(\mu = 10, \sigma = 2)$ where $\mu = 10$ (mean) and $\sigma = 2$ (standard deviation).

2. Find the probability that the nurse will complete the task within 8 to 10 minutes.

   This requires calculating the probability $P(8 \leq T \leq 10)$.

   To do this, we will convert the time into the Z-scores using the formula: $Z = \frac{X - \mu}{\sigma}$ For $X = 8$ minutes: $Z_1 = \frac{8 - 10}{2} = \frac{-2}{2} = -1$ For $X = 10$ minutes: $Z_2 = \frac{10 - 10}{2} = 0$

3. Find the corresponding probabilities:

   Using standard normal distribution tables:

   • The probability corresponding to $Z = -1$ is approximately 0.1587.
   • The probability corresponding to $Z = 0$ is 0.5.

4. Calculate the final probability: The probability that the nurse completes the task within 8 to 10 minutes is: $P(8 \leq T \leq 10) = P(Z_2) - P(Z_1) = 0.5 - 0.1587 = 0.3413$

Thus, the probability that the nurse completes the task in 8 to 10 minutes is approximately 0.3413 or 34.13%.

Would you like further details on this solution or have any other questions?

Here are 5 related questions to explore further:

1. How do we interpret Z-scores in a normal distribution?
2. What is the empirical rule in the context of normal distributions?
3. How can we use the cumulative distribution function (CDF) to find probabilities in normal distribution?
4. What is the significance of the mean and standard deviation in normal distribution problems?
5. How do we apply normal distribution in real-life healthcare scenarios?

Tip: For normal distribution problems, always convert raw data points to Z-scores for easy calculation of probabilities using standard normal tables.