A company sells apples in packages of 444. The masses of the individual apples are normally distributed with a mean of 175\,\text{g}175g175, start text, g, end text and a standard deviation of 15\,\text{g}15g15, start text, g, end text. Assume that the weights of apples are independent from each other.

By calculating the shaded area by integrating with lower boundary condition 736 and upper boundary condition 9999 the probability P(T > 786) is 0.12.

Given :

A company sells apples in packages of 4.
The masses of the individual apples are normally distributed with a mean of 175g and a standard deviation of 15g.
Let T be the total weight of the randomly selected apples.
Assume that the weights of apples are independent of each other.

The mean of T is given by :

[tex]\mu_T = 175 + 175+ 175+175[/tex]

[tex]\mu_T = 700[/tex]

The standard deviation of T is given by:

[tex]\sigma^2_T = 15^2+15^2+15^2+15^2[/tex]

[tex]\sigma^2_T = 4\times 15^2[/tex]

[tex]\sigma_T = 30[/tex]

For determining the probability P(T > 736) find the shaded area above T = 736.

By calculating the shaded area by integrating with lower boundary condition 736 and upper boundary condition 9999 the probability P(T > 786) can be determined.

P(T > 736) [tex]\approx[/tex] 0.12

So, the correct option is given by D).

For more information, refer to the link given below:

https://brainly.com/question/11234923