Answer:
The sample size required is 102.
Step-by-step explanation:
The (1 - α)% confidence interval for population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
Given:
σ = 9.2
(1 - α)% = 90%
MOE = 1.5
The critical value of z for 90% confidence level is:
[tex]z_{0.10/2}=1.645[/tex]
*Use a z-table.
Compute the value of n as follows:
[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
   [tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]
     [tex]=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102[/tex]
Thus, the sample size required is 102.
