Question

To determine the wind speed in a certain location, 40 samples are taken in a limited period of time. The average value of the measurements is 30 miles per hour, and the standard deviation of the sample is 2 miles per hour. Determine a 95% confidence interval for the mean value of the wind speed.

Answer 1

Answer: 95% confidence interval is (29.38, 30.62).

Step-by-step explanation:

Since we have given that

n = Sample size = 40

Average value = 30 miles per hour

Standard deviation = 2 miles per hour

We need to find the interval for 95% confidence interval.

So, z = 1.96

So, the intervals would be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=30\pm 1.96\times \dfrac{2}{\sqrt{40}}\\\\=30\pm 0.62\\\\=(30-0.62,30+0.62)\\\\=(29.38,30.62)$

Hence, 95% confidence interval is (29.38, 30.62).