sc1 t3 7 8 9 • Name:

lap (s)
168
162
158
164
153
143

Part I: Chapter 7

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.

1. n = _________ Determine the sample size n for the data.
2. x = _________ Determine the sample mean x for the data.
3. sx = _________ Determine the sample standard deviation sx for the data.
4. p(lap ≤ 158) = _________ Calculate the probability that a lap will be 158 seconds or less.
5. 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.
6. 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.
7. 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.
8. 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.
9. df = _________ Calculate the number of degrees of freedom.
10. tc = _________ Calculate tcritical using a 95% level of confidence.
11. E = _________ Calculate the margin of error for the mean E.
12. p(__________ ≤ μ ≤ __________) = 0.95 Calculate the 95% confidence interval for the population mean μ.