contestada

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?

Respuesta :

Felecityyy
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
fichoh

The mean and standard deviation of the sample of orange sweets can be ibtaide using the binomial approximation relation. Hence, the mean and standard deviation are 13.75 and 2.905

Mean = np

  • Sample size, n = 25
  • Proportion, p

Dynamite mints :

  • 25 x 0.1 = 2.5

Holiday mints:

  • 25 x 0.45 = 11.25

Total orange candies = (2.5 + 11.25) = 13.75

2.)

Standard deviation, σ = √(npq)

  • q = 1 - p

Dynamite mints :

√[25 x 0.1 × (1 - 0.1)] = 1.5

Holiday mints :

√[25 x 0.45 (1 - 0.45)] = 2.4874

Combined standard deviation : s²(x + y) = s²(x) + s²(y)

Std = √(1.5²2 + 2.4874²) = 2.905

Therefore, the mean and sample standard deviation are 13.75 and 2.905 respectively.

Learn more : https://brainly.com/question/8165716