The actual weights of bags of pet food are normally distributed.The mean of the weights is 50.0lb,with a standard deviation of 0.2lb.
Sketch a normal cuve for the distribution.Label the x-axis at one,two,and three standard feciation from the mean,in addition label all the percentages and the values.
http://www.regentsprep.org/Regents/math/algtrig/ATS2/NormalLesson.htm
To sketch a normal curve, you will need to follow these steps:
1. Determine the boundaries: Start by identifying the values for one, two, and three standard deviations from the mean. In this case, we have:
- One standard deviation: Mean - (1 * Standard Deviation) = 50.0 - (1 * 0.2) = 49.8 lb
- Two standard deviations: Mean - (2 * Standard Deviation) = 50.0 - (2 * 0.2) = 49.6 lb
- Three standard deviations: Mean - (3 * Standard Deviation) = 50.0 - (3 * 0.2) = 49.4 lb
2. Determine the percentages: Based on the properties of a normal distribution, you can assign percentages to each standard deviation. Generally, in a normal distribution:
- One standard deviation covers approximately 68% of the data
- Two standard deviations cover approximately 95% of the data
- Three standard deviations cover approximately 99.7% of the data.
3. Draw the x-axis: Draw a horizontal line where you will plot the values of the pet food weights.
4. Plot the values: Place tick marks on the x-axis at the boundaries you calculated earlier: 49.4 lb, 49.6 lb, 49.8 lb, and the mean 50.0 lb.
5. Label the x-axis: Label the tick marks on the x-axis with the corresponding values (49.4, 49.6, 49.8, and 50.0 lb).
6. Label the percentages: Above each tick mark, add labels indicating the percentages of data within each standard deviation. For example, above the mean (50.0 lb), you can label it as the "Mean (50.0 lb)". Above the tick mark at 49.8 lb, you can label it as "68%". Above the tick mark at 49.6 lb, label it as "95%", and above the tick mark at 49.4 lb, label it as "99.7%".
7. Sketch the curve: Sketch a smooth curve connecting the plotted values, which starts at the mean (50.0 lb) and gradually falls as it moves towards the edges.
Remember that the normal distribution is symmetrical, so the curve will mirror itself on both sides of the mean.
By following these steps, you should be able to correctly sketch the normal curve for the given pet food weight distribution.