# As part of an annual review of its accounts, a discount brokerage selects a random sample of 28 customers. Their accounts are reviewed for total account valuation, which showed a mean of $35,100, with a sample standard deviation of$8,800. What is a 98\% confidence interval for the mean account valuation of the population of customers?

As part of an annual review of its accounts, a discount brokerage selects a random sample of 28 customers. Their accounts are reviewed for total account valuation, which showed a mean of $35,100, with a sample standard deviation of$8,800. (Use t Distribution Table.)
What is a $98\mathrm{%}$ confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.)
$98\mathrm{%}$ confidence interval for the mean account valuation is between $and$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

beljuA
Step 1
The provided information are:
Sample size $\left(n\right)=28$
Sample mean $\left(\stackrel{―}{x}\right)=\mathrm{}35,100$
Sample standard deviation $\left(s\right)=\mathrm{}8,800$
Step 2
The formula to calculate the confidence interval for population mean is:
$\stackrel{―}{x}±{t}_{\left(\frac{\alpha }{2},df\right)}\frac{s}{\sqrt{n}}$
Step 3
Here, the population standard deviation is unknown. So, the t-critical value is used.
The degrees of freedom is: $df=n-1=28-1=27$
The critical value for $98\mathrm{%}$ confidence level at $df=27$ can be found using the t-table. That is,
${t}_{\left(\frac{\alpha }{2},df\right)}={t}_{\left(\frac{0.02}{2},27\right)}$
$=2.473$
Step 4
Substitute the values in the confidence interval formula.
$CI=\stackrel{―}{x}±{t}_{\left(\frac{\alpha }{2},df\right)}\frac{s}{\sqrt{n}}$
$=35100±2.473×\frac{8800}{\sqrt{28}}$
$=35100±4112.141$
$=\left(30987.859,39212.141\right)$
$\approx \left(30988,39212\right)$
Step 5
Thus, the $98\mathrm{%}$ confidence interval for the mean account valuation is between $30988 and$39212.