Let's solve the problem step by step.

(a) Point Estimate of the Population Mean

The point estimate of the population mean is simply the sample mean of the data. To calculate it, we sum all the values of units sold and then divide by the number of months.

Given data for units sold over 5 months:

• $x_1 = 96$
• $x_2 = 96$
• $x_3 = 86$
• $x_4 = 93$
• $x_5 = 99$

The sample mean ($\bar{x}$) is:

$\bar{x} = \frac{x_1 + x_2 + x_3 + x_4 + x_5}{5} = \frac{96 + 96 + 86 + 93 + 99}{5} = \frac{470}{5} = 94$

So, the point estimate of the population mean is 94 units sold per month.

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(b) Point Estimate of the Population Standard Deviation

The sample standard deviation ($s$) is given by the formula:

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$

Where:

• $n = 5$ (number of months)
• $\bar{x} = 94$ (sample mean)

Let's calculate it step by step.

1. Calculate the differences from the mean for each data point:

   • $96 - 94 = 2$
   • $96 - 94 = 2$
   • $86 - 94 = -8$
   • $93 - 94 = -1$
   • $99 - 94 = 5$

2. Square these differences:

   • $2^2 = 4$
   • $2^2 = 4$
   • $(-8)^2 = 64$
   • $(-1)^2 = 1$
   • $5^2 = 25$

3. Sum the squared differences: $4 + 4 + 64 + 1 + 25 = 98$

4. Divide by $n-1$ (which is 4): $\frac{98}{4} = 24.5$

5. Take the square root to find the standard deviation: $s = \sqrt{24.5} \approx 4.95$

So, the point estimate of the population standard deviation is 4.95 units.

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Summary:

• (a) The point estimate of the population mean is 94 units sold per month.
• (b) The point estimate of the population standard deviation is 4.95 units.

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Do you want more details on the calculations or have any other questions?

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Here are 5 related questions you might be interested in:

1. How can we calculate a confidence interval for the population mean?
2. What is the difference between sample standard deviation and population standard deviation?
3. How would the standard deviation change if the dataset included more months?
4. What is the relationship between variance and standard deviation?
5. How can we test whether this sample mean is significantly different from a hypothesized population mean?

Tip: Always check whether you are using a sample or population when calculating standard deviation, as the formulas slightly differ.