The average annual wind speed in Rochester, Minnesota is 13.1 miles per hour. A sample of...

The average annual wind speed in Rochester, Minnesota is 13.1 miles per hour. A sample of 100 days is used to determine the average wind speed. Find the 98% confidence interval of the mean. Assume the standard deviation was 2.8 miles per hour.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = =13.1

Population standard deviation = = 2.8

Sample size = n =100

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 2.326 * ( 2.8 / $\sqrt$ 100 )

= 0.65
At 98% confidence interval mean
is,

- E < < + E

13.1 - 0.65 < < 13.1 + 0.65

12.45 < < 13.75

orchestra answered 2 years ago

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