IM3.7.6 Exit Ticket

Lind, Jon

Gas Mileage

A normal curve is a smooth curve that is symmetric and bell shaped. Data distributions that are mound shaped are often modeled using a normal curve, and we say that such a distribution is approximately normal. One example of a distribution that is approximately normal is the distribution of compy heights from the example we did in class. Distributions that are approximately normal occur in many different settings. For example, a salesman kept track of the gas mileage for his car over a 25-week span. The mileages (miles per gallon rounded to the nearest whole number) were 23, 27, 27, 28, 25, 26, 25, 29, 26, 27, 24, 26, 26, 24, 27, 25, 28, 25, 26, 25, 29, 26, 27, 24, 26. 1. Use technology to find the mean and standard deviation of the mileage data.

2. Calculate the relative frequency of each of the mileage values. For example, the mileage of 26 mpg has a frequency of 7. To find the relative frequency, divide 7 by 25, the total number of mileages recorded. 3. Complete the following table:
4. Construct a relative frequency histogram using the scale below. Draw a smooth curve (using polyline) that comes reasonably close to passing through the midpoints of the tops of the bars in the histogram. 5. Mark the mean on the histogram with a vertical line. Mark one standard deviation to the left and right of the mean. Shade the area of the histogram that represents the proportion of mileages that are within one standard deviation of the mean.

6. Describe the shape of the mileage distribution. 7. Find the proportion of the data within one standard deviation of the mean.