Question

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

Answer 1

Lower limit = 1007.95 cm/s

Upper limit = 1142.05 cm/s

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:

`M-z*\sigma/√(n) \leq\mu\leq M+z*\sigma/√(n)`

For a 95% CI, the value of z=1.96.

`1075-1.96*265/√(60) \leq\mu\leq 1075+1.96*265/√(60) \\\\1075-67.05 \leq\mu\leq 1075+67.05\\\\ 1007.95 \leq\mu\leq 1142.05`