Ten percent of all dynamite mints candies are orange and 45 percent of all holiday mints candies are orange. two independent random samples, each of size 25, are selected⎯one from dynamite mints candies and the other from holiday mints candies. the total number of orange candies in the two samples is observed. what are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?

The answers are 13.75 and 2.905.

1.) To get the total number of orange candies, we must multiply the given percentage to the size of the samples. Then, add the products.

Dynamite mints - 25 x 10% = 2.5

Holiday mints - 25 x 45% = 11.25

Total orange candies - 2.5 + 11.25 = 13.75

2.) To get the standard deviation, we will first find the standard deviation of each sample. Use this formula: standard deviation = √[np (1-p) ] The variable n is the size of the sample while the p is the probability or percentage.

Dynamite mints - √[25 x 10% (1 - 10%) ] = 1.5

Holiday mints - √[25 x 45% (1 - 45%) ] = 2.4874 ...

After getting the standard deviations, we'll combine then using s^2 (x + y) = s^2 (x) + s^2 (y)

Standard deviation of orange candies = std of dynamite + std of holiday

Std = √ (1.5^2 + 2.4874 ... ^2) = √8.4375 ... = 2.9046 or 2.905