A meteorologist sampled 10 thunderstorms found that the aver

A meteorologist sampled 10 thunderstorms found that the average speed at which they traveled across a certain state was 13 miles per hour. The standard deviation of the sample was 4.4 miles per hour. Round the final answers to two decimal places. Find the 95% confidence interval of the mean. Assume that the variable is normally distributed. ? < u < ?

If a meteorologist wanted to use the highest speed to predict the times it would take the storms to travel across the state in order to issue warnings, what figure would the meteorologist likely use?

The meteorologist should use ? miles per hour for the prediction.

Solution

CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=13
Standard deviation( sd )=4.4
Sample Size(n)=10
Confidence Interval = [ 13 ± t a/2 ( 4.4/ Sqrt ( 10) ) ]
= [ 13 - 2.262 * (1.391) , 13 + 2.262 * (1.391) ]
= [ 9.853,16.147 ]