At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, σ can be assumed to be 270 cm/sec. Find a 95% confidence interval for the population mean wind speed at this site.

Answer: [tex](1006.68\ cm/sec,\ 1143.32\ cm/sec)[/tex]Step-by-step explanation:As per given we have,n=60[tex]\overline{x}=1075\ cm/sec\\\\ \sigma=270\ cm/sec[/tex]Critical value for 95% confidence : [tex]z_{\alpha/2}=1.96[/tex]Confidence interval :[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=1075+(1.96)\dfrac{270}{\sqrt{60}}\\\\\approx1075\pm68.3194\\\\=(1075-68.32,\ 1075+68.32)\\\\= (1006.68,\ 1143.32)[/tex]Hence, a 95% confidence interval for the population mean wind speed at this site. = [tex](1006.68\ cm/sec,\ 1143.32\ cm/sec)[/tex]