MATH SOLVE

3 months ago

Q:
# At winds 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 of 1075 cm/sec and based on long term experience the standard deviation for wind speed is 265 cm/sec. Round answers to two decimal places, if necessary(a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.)lower limit cm/secupper limit cm/sec

Accepted Solution

A:

Answer:Lower limit = 1007.95 cm/sUpper limit = 1142.05 cm/sStep-by-step explanation:We have to calculate a 95% CI with population's standard deviation known.The sample is size n=60, with mean M=1075.The confidence interval can be expressed as:[tex]M-z*\sigma/\sqrt{n} \leq\mu\leq M+z*\sigma/\sqrt{n}[/tex]For a 95% CI, the value of z=1.96.[tex]1075-1.96*265/\sqrt{60} \leq\mu\leq 1075+1.96*265/\sqrt{60} \\\\1075-67.05 \leq\mu\leq 1075+67.05\\\\ 1007.95 \leq\mu\leq 1142.05[/tex]