Answer:
The 99% confidence interval for population mean μ is (24.90, 29.10).
Step-by-step explanation:
Let the random variable X is defined as the lengths of text messages.
It is provided that X follows a Normal distribution with an unknown population mean μ and standard deviation σ = 4.
The (1 - α) % confidence interval for population mean is:
[tex]CI=\bar x\pm z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}[/tex]
Given:
[tex]n=24\\\bar x=27\\z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.576[/tex]
Compute the 99% confidence interval for μ as follows:
[tex]CI=\bar x\pm z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}\\=27\pm 2.576\times\frac{4}{\sqrt{24}} \\=27\pm 2.1033\\=(24.8967, 29.1033)\\\approx(24.90, 29.10)[/tex]
Thus, the 99% confidence interval for population mean μ is (24.90, 29.10).
