Question

Ur cool if u answer this correctly with working

Answer 1

Add up all the frequencies to the get the total number of occurrences:

2 + 2 + 16 + 10 + 9 + 4 + x + 2 = x + 45

Then the probability corresponding to a given frequency is equal to (frequency)/(sum of frequencies). For example, the probability that a randomly chosen student has read 1 book in the marathon is 2/(x + 45); the probability of having read 4 books is 10/(x + 45); etc.

The mean is computed by multiplying each book count by their respective probability, and adding these all up. If the mean is 4.28, then

`1\cdot\frac2{x+45} + 2\cdot\frac2{x+45} + 3\cdot(16)/(x+45) + \cdots + 8\cdot\frac2{x+45} = 4.28`

Simplifying the left side gives

`(2+4+48+40+45+24+7x+16)/(x+45) = 4.28 \\\\ (7x+179)/(x+45) = 4.28`

Solve for x :

`7x+179 = 4.28(x+45) \\\\ 7x+179 = 4.28x + 192.6 \\\\ 2.72x = 13.6 \\\\ \boxed{x = 5}`