Question

A meteorologist is studying the speed at which thunderstorms travel. A sample of 10 storms are observed. The mean of the sample was 12.2 MPH and the standard deviation of the sample was 2.4. What is the 95% confidence interval for the true mean speed of thunderstorms?

Answer 1

The 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].

Explanation:

Given information:

Sample size = 10

Sample mean = 12.2 mph

Standard deviation = 2.4

Confidence interval = 95%

At confidence interval 95% then z-score is 1.96.

The 95% confidence interval for the true mean speed of thunderstorms is

`CI=\overline{x}\pm z*(s)/(√(n))`

Where,
`\overline{x}` is sample mean, z* is z score at 95% confidence interval, s is standard deviation of sample and n is sample size.

`CI=12.2\pm 1.96(2.4)/(√(10))`

`CI=12.2\pm 1.487535`

`CI=12.2\pm 1.488`

`CI=[12.2-1.488, 12.2+1.488]`

`CI=[10.712, 13.688]`

Therefore the 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].