In a class of 40 students, the mean score of the girls is 30, the mean score of the boys is 40, and the mean score of the entire class is 32. If the score of one boy was incorrectly computed as 30 for 40, what is the correct mean score for the entire class?22 Mark For ReviewA) 31B) 31.50C) 32.25D) 36

To solve this problem, we first need to find out the number of boys and girls in the class.

We know that the mean score of the entire class is 32. The mean is calculated by dividing the total sum of all scores by the number of students. So, the total sum of all scores is 32 * 40 = 1280.

We also know that the mean score of the girls is 30 and the mean score of the boys is 40. Let's assume the number of girls is x and the number of boys is y. So, we have:

30x + 40y = 1280

We also know that the total number of students is 40, so:

x + y = 40

We can solve these two equations to find the values of x and y.

From the second equation, we can express y as 40 - x. Substituting this into the first equation gives:

30x + 40(40 - x) = 1280 30x + 1600 - 40x = 1280 10x = 320 x = 32

Substituting x = 32 into the second equation gives y = 40 - 32 = 8.

So, there are 32 girls and 8 boys in the class.

Now, we know that one boy's score was incorrectly computed as 30 instead of 40. So, the total sum of all scores should be increased by 10. The new total sum is 1280 + 10 = 1290.

The correct mean score for the entire class is the total sum divided by the number of students, which is 1290 / 40 = 32.25.

So, the correct answer is C) 32.25.