Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
the table shows a sample of the maximum capacitymaximum number of spectatorsof 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.
- 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. HintOrder 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?
OpenStax Statistics, 6.2 Using the Normal Distribution, exercise 53