The weight of the fish in a certain lake are normally distributed with a mean of 11 pounds and a standard deviation of 11 pounds if 25 fish are randomly selected what is the probability that their mean will be above 16 pounds

The probability that their mean will be above 16 pounds is 0.0116.

Step-by-step explanation:

We are given that the weight of the fish in a certain lake are normally distributed with a mean of 11 pounds and a standard deviation of 11 pounds.

Also, 25 fish are randomly selected.

Let = sample mean weight

The z-score probability distribution for sample mean is given by;

                Z =  ~ N(0,1)

where, = mean weight = 11 pounds

             = standard deviation = 11 pounds

            n = sample of fish = 25

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that their mean will be above 16 pounds is given by = P( > 16 pounds)

         P( > 16) = P( > ) = P(Z > 2.27) = 1 - P(Z 2.27)

                                                      = 1 - 0.9884 = 0.0116

The above probability is calculated by looking at the value of x = 2.27  in the z table which has an area of  0.9884.

Therefore, if 25 fish are randomly selected, the probability that their mean will be above 16 pounds is 0.0116.

there is no diagram : /

step-by-step explanation:

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'.