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ser-zykov [4K]
3 years ago
11

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?
Mathematics
1 answer:
dezoksy [38]3 years ago
4 0

Answer:

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

Step-by-step 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*\frac{s}{\sqrt{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\frac{2.4}{\sqrt{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].

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