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
[tex]CI=\overline{x}\pm z*\frac{s}{\sqrt{n}}[/tex]
Where, [tex]\overline{x}[/tex] is sample mean, z* is z score at 95% confidence interval, s is standard deviation of sample and n is sample size.
[tex]CI=12.2\pm 1.96\frac{2.4}{\sqrt{10}}[/tex]
[tex]CI=12.2\pm 1.487535[/tex]
[tex]CI=12.2\pm 1.488[/tex]
[tex]CI=[12.2-1.488, 12.2+1.488][/tex]
[tex]CI=[10.712, 13.688][/tex]
Therefore the 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].
