On Monday evening 26 March I had my son run a set of laps at the Pohnpei state track at a pace of his own choice. I timed the laps using a stopwatch. The laps are the first set of multiple laps of his that I have timed. As there are no pre-existing lap times, this analysis looks at his theoretic capabilities based on the data. Pretend that the data is normally distributed.
n = _________ Determine the sample size n for the data.
x = _________ Determine the sample mean x for the data.
sx = _________ Determine the sample standard deviation sx for the data.
p(lap ≤ 158) =
_________ Calculate the probability that a lap will be 158 seconds or less.
p(lap ≥ 164) =
_________ On 29 November 2011 I ran a set of laps with a mean time of 164 seconds. Use the normal distribution function NORMDIST to calculate the probability that my son's lap time would be 164 seconds or more.
p(lap ≤ __________) = 0.10
Use the normal distribution inverse function NORMINV to calculate the lap time BELOW which are found the 10% lowest lap times (fastest laps).
Part II: Chapter 8 Use the sample size and standard deviation from part I.
SE = _________ Calculate the standard error of the mean for the lap times data.
Part III: Chapter 9.12 Use the data and results above in this section.
p(__________ ≤ μ ≤ __________) = 0.68 As in quiz 08, use the mathematics of section 9.12 to calculate the 68% confidence interval for the population mean μ.
Part IV: Chapter 9.2 Use the data and results above in this section.
df = _________ Calculate the number of degrees of freedom.
t_{c} = _________ Calculate t_{critical} using a 95% level of confidence.
E = _________ Calculate the margin of error for the mean E.
p(__________ ≤ μ ≤ __________) = 0.95 Calculate the 95% confidence interval for the population mean μ.