The weight of apples is normally distributed. Large apples have a mean of 15 oz and medium apples have a mean of 10 oz. The standard deviation of the weight of both large and medium apples is 2 oz. You select a large apple and a medium apple at random. Let L be the weight of the large apple and M be the weight of a medium apple. Let X be the total weight of the two apples (X = L + M). The distribution of X is also normal.

Required:
a. Use the rules for means and variances to find the mean and standard deviation of X.
b. What is the probability that the total weight X is between 22 and 28 oz?

a) X has a mean of 25 and a variance of 8.

b) The probability that the total weight X is between 22 and 28 oz is 0.711.

Step-by-step explanation:

We have to calculate the mean and variance of a sum of random normal variables.

We can apply the rule for mean and variance for sum of independent variables:

Then, the mean and variance of X is:

We can calculate the probability that X is between 22 and 28 as:

46 dollars is the answer.

step-by-step explanation:

6*6 = 36,         36+10=46

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)