Respuesta :
Answer:
The 99% confident that the population mean (μ) falls between 34.73 and 36.86.
Step-by-step explanation:
Consider the provided information.
The formula used for confidence interval on the true mean is:
[tex]\bar{x}\pm t_{n-1}\frac{s}{\sqrt{n}}[/tex]
It is given that mean is 35.8, standard deviation is 2.5, Sample size is 40.
As the sample size is 40 and confidence interval is 99%. Therefore the value of [tex]t_{n-1}=2.70[/tex].
Now, substitute the respective values in the above formula.
[tex]35.8\pm 2.70\times \frac{2.5}{\sqrt{40}}[/tex]
[tex]35.8\pm 2.70\times \frac{2.5}{6.32}[/tex]
[tex]35.8\pm 2.70\times 0.396[/tex]
[tex]35.8\pm 1.068[/tex]
[tex]35.8+1.068[/tex] or [tex]35.8-1.068[/tex]
[tex]36.86[/tex] or [tex]34.73[/tex]
Hence, the 99% confident that the population mean (μ) falls between 34.73 and 36.86.
