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Card 20 / 25:
shows a sample of the maximum capacity (maximum number of spectators) of sports stadiums. The table does not include horse-racing or motor-racing stadiums. 40,000 40,000 45,050 45,500 46,249 48,134 49,133 50,071 50,096 50,466 50,832 51,100 51,500 51,900 52,000 52,132 52,200 52,530 52,692 53,864 54,000 55,000 55,000 55,000 55,000 55,000 55,000 55,082 57,000 58,008 59,680 60,000 60,000 60,492 60,580 62,380 62,872 64,035 65,000 65,050 65,647 66,000 66,161 67,428 68,349 68,976 69,372 70,107 70,585 71,594 72,000 72,922 73,379 74,500 75,025 76,212 78,000 80,000 80,000 82,300
Calculate the sample mean and the sample standard deviation for the maximum capacity of sports stadiums (the data).Construct a histogram.Draw a smooth curve through the midpoints of the tops of the bars of the histogram.In words, describe the shape of your histogram and smooth curve.Let the sample mean approximate μ and the sample standard deviation approximate σ . The distribution of X can then be approximated by X ~ _____(_____,_____).Use the distribution in part e to calculate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators.Determine the cumulative relative frequency that the maximum capacity of sports stadiums is less than 67,000 spectators. Hint: Order the data and count the sports stadiums that have a maximum capacity less than 67,000. Divide by the total number of sports stadiums in the sample.Why aren’t the answers to part f and part g exactly the same?
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