6.7 Project: Normal Distribution

Write neatly and work in sequential order. Please answer the following questions in order.
Data
The following tables provide lap times from Terri Vogel’s log book. Times are recorded in seconds for 2.5-mile laps completed in a series of races and practice runs.
Lap 1Lap 2Lap 3Lap 4Lap 5Lap 6Lap 7Race 1135130131132130131133Race 2134131131129128128129Race 3129128127127130127129Race 4125125126125124125125Race 5133132132132131130132Race 6130130130129129130129Race 7132131133131134134131Race 8127128127130128126128Race 9132130127128126127124Race 10135131131132130131130Race 11132131132131130129129Race 12134130130130131130130Race 13128127128128128129128Race 14132131131131132130130Race 15136129129129129129129Race 16129129129128128129129Race 17134131132131132132132Race 18129129130130133133127Race 19130129129129129129128Race 20131128130128129130130Collect the Data
1. Use a stratified sampling method by lap (laps 1 through 7) and a random number generator to pick six race times from each stratum. Record the sample lap times for laps two to seven . This means select 6 random times from lap 2, another 6 random times from lap 3, and so on.
Lap 2Lap 3Lap 4Lap 5Lap 6Lap 7____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Analyze the Data
2. Construct a frequency table by using the intervals below. Then sketch the histogram.
TimesFrequency124 – 125126 – 127 128 – 129 130 – 131 132 – 133 134 – 135 3. Calculate the following (where x = lap times [in seconds]):
a. x¯¯¯x¯ = _______
b. ss = _______
4. Construct a histogram for the frequency table above.
5. Draw a smooth curve through the tops of the bars of the histogram. Write one to two complete sentences to describe the general shape of the curve. (Keep it simple. Does the graph go straight across, does it have a v-shape, does it have a hump in the middle or at either end, and so on?)
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