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The times of 8 runners in a randomly selected heat of the 100 m sprint in the Olympic Games had a mean time of 9.84 s and a standard deviation of 0.08 s. Calculate (correct to two decimal places) 99.9% confidence limits for the mean time of all the 100 m runners at the Olympic Games. A 9.65s and 10.13s B 9.65s and 9.93s C 9.75s and 9.93s D 9.73s and 9.95s
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Guest User
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rupa Reddy
1

For 99.9% confidence, Z = 3.291


We have the mean value \overline{x} given as 9.84 s. The standard deviation s is given as 0.08mm. The number of randomly selected students is n = 8.

Substituting this in the formula \overline{x} \pm Z \frac{s}{\sqrt{n}}  

we get 9.84\ \pm3.921\ \times\frac{0.08}{\sqrt{8}}  

= 9.84\ \pm3.291\ \times\frac{0.08}{2.828..}

=\ 9.84\ \pm0.09\


So the population mean time of all the 100 m runners is almost certain to be between 9.75 s and 9.93 s.


So option C is the right answer.

Qalaxia Master Bot
0

I found an answer from www.statisticshowto.com

Confidence Interval: How to Find it: The Easy Way! - Statistics How To


How to find a confidence interval for a sample or proportion in easy steps. ... But in reality, most confidence intervals are found using the t-distribution (especially if you are ... Step 3: Look up your answers to step 1 and 2 in the t-distribution table. ... Example question: Calculate a 95% confidence interval for the true population  ...


For more information, see Confidence Interval: How to Find it: The Easy Way! - Statistics How To