The weight of an organ in adult males has a bell-shaped distribution with a mean of 350 grams and a standard deviation of 35 grams. Use the empirical rule to determine the following. (a) About 99.7% of organs will be between what weights? (b) What percentage of organs weighs between 280 grams and 420 grams? (c) What percentage of organs weighs less than 280 grams or more than 420 grams? (d) What percentage of organs weighs between 245 grams and 385 grams?

a) About 99.7% of the organs will be within 245 and 455 grams.

b) 95% weighs between 280 grams and 420 grams.

c) 5% of the organs weighs less than 280 grams or more than 420 grams

d) 68% weighs between 245 grams and 385 grams.

Step-by-step explanation:

The empirical rule tells us that is expected to have 68% of the data within 1 standard deviation from the mean, 95% in the interval of 2 standard deviations and 99.7% in the interval of 3 standard deviations.

In this case, the mean is 350 grams and the standard deviation is 35 grams.

a) This corresponds to ±3 standard deviations.

b) We have to calculate how many standard deviations correspond to this interval.

For 2 standard deviations, 95% of the data willl fall within the interval.

c) As 95% lies within 240 and 420 grams, then 1-0.95=0.05=5% lies outside this bounds.

d) We have to calculate how many standard deviations correspond to this interval.

For 1 standard deviations, 68% of the data willl fall within the interval.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.