Questions: Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 90% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required? 240 194 181 159 157 156 148 148 148 148 What is the confidence interval estimate of the population mean μ ? million < μ < million (Round to one decimal place as needed.)

Solution Steps

The mean net worth of the ten wealthiest celebrities is calculated as follows:

\[ \mu = \frac{\sum_{i=1}^{N} x_i}{N} = \frac{1679}{10} = 167.9 \]

The sample standard deviation is calculated using the formula:

\[ s = \sqrt{\frac{\sum (x_i - \mu)^2}{n-1}} = \sqrt{886.1} = 29.8 \]

To construct the 90% confidence interval for the population mean, we use the formula:

\[ \bar{x} \pm t \frac{s}{\sqrt{n}} \]

Where:

• \(\bar{x} = 167.9\) (sample mean)
• \(t \approx 1.8\) (t-value for 90% confidence level with \(n-1 = 9\) degrees of freedom)
• \(s = 29.8\) (sample standard deviation)
• \(n = 10\) (sample size)

Calculating the confidence interval:

\[ 167.9 \pm 1.8 \cdot \frac{29.8}{\sqrt{10}} = (150.6, 185.2) \]

Final Answer