Respuesta :
Given Information:
Mean time to finish 400 meter dash = μ = 65 seconds
Standard deviation to finish 400 meter dash = σ = 2.5 seconds
Confidence level = 95%
Required Information:
95% confidence interval = ?
Answer:
[tex]CI = 60 \: to \: 70 \: seconds[/tex]
Step-by-step explanation:
In the normal distribution, the empirical rule states approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.
The confidence interval for 95% confidence limit is given by
[tex]CI = \mu \pm 2\sigma[/tex]
Since approximately 95% of all the data lie within 2 standard deviations from the mean. μ is the mean time Carson takes to finish 400 meter dash and σ is the standard deviation.
[tex]CI = 65 \pm 2(2.5)[/tex]
[tex]CI = 65 \pm 5[/tex]
[tex]CI = 65 - 5 \: to \: 65 + 5[/tex]
[tex]CI = 60 \: to \: 70 \: seconds[/tex]
Therefore, the 95% confidence interval is between 60 to 70 seconds
What does it mean?
It means that we are 95% confident that the Carson's mean to finish 400 meter dash is within the interval of (60, 70).
