normal distributionMy highlightsNormal Distribution (Lap Times)Class Time:Names:Student Learning Outcome• The student will compare and contrast empirical data and a theoretical distribution to determine ifTerry Vogel's lap times fit a continuous distribution.DirectionsRound the relative frequencies and probabilities to four decimal places. Carry all other decimal answers totwo places.Collect the Data1. Use the data from Appendix C. Use a stratified sampling method by lap (races 1 to 20) and a randomnumber generator to pick six lap times from each stratum. Record the lap times below for laps twoto seven.7:47 AM25 X45°F Cloudy11/11/202111II Lap2Nace 13H 14Pace 15Nacenace 17ace 18Ree 20MixGramTie Ca38EBSS SSEE111111111

Ans: 3. Mean =129.64 std. deviation s=2.37 The above data is normally distributed. The interquartile range (IQR) is the difference between the third and the first quartiles. It is a measure of dispersion. Lower quartile (xL): 128Upper quartile (xU): 131 Interquartile range (xU-xL): 3 Sorted Data Set: 134, 134, 133, 133, 133, 132, 132, 131, 131, 131, 131, 131, 131, 130, 130, 130, 130, 130, 130, 130, 129, 129, 129, 129, 128, 128, 128, 128, 128, 128, 127, 127, 126, 126, 125, 125 Median=130 .The p- th percentile is a value such that at least pp percent of the observations are less than or equal to this value and at least (100?p) percent of the observations are greater than or equal to this value. 15th percentile P(X<x)=0.15 z=-1.036 z=(x-129.64)/2.37 -1.036*2.37+129.64=x x=127.18 85th percentile z=1.036 x=1.036*2.37+129.64=132.09 P(X>130)=P(z>0.1519)=1-P(z<0.1519)=1-0.56=0.44 85 th percentile means that 85 % of the lap times are below the specific lap time