[Statistics] Calculate the percentage

[LokLe]

Homework Statement

Suppose the average mark of a class in a test is 85. At most what percentage of the
students have got marks not lower than 90?

Relevant Equations

Markov's Inequality: P(X >= a) = E(X)/a

My attempt:

P(x>=90) = 85/90 = 17/18

Is my understanding of the equation correct? Thanks

 

[PeroK]

Looks right. Strange question!

 

[chwala]

Looks right. Strange question!

How does it look right @PeroK?
Can you at least kindly substantiate...you're considering confidence level or what...

 

[WWGD]

If you were given the standard deviation, you could use here Chebyshev inequality. https://en.m.wikipedia.org/wiki/Chebyshev's_inequality
Other than that, yes, Markov's inequality holds up, but it's not an equality.
Rather, $P(X\geq a)\leq \frac{E(X)}{a}$, for $X\geq 0$ a random variable https://en.m.wikipedia.org/wiki/Markov's_inequality

 

[pasmith]

Homework Statement: Suppose the average mark of a class in a test is 85. At most what percentage of the
students have got marks not lower than 90?
Relevant Equations: Markov's Inequality: P(X >= a) = E(X)/a

My attempt:

P(x>=90) = 85/90 = 17/18

Is my understanding of the equation correct? Thanks

If you are asked for a percentage, you should express your answer as a percentage, ie. as $94.\bar{4}\,\%$ rather than $\frac{17}{18}$.