Step 1

Given:

The range of uniform distribution is between 5 to 7 years.

The objective is to find the probability of randomly chosen student who will stay at most 6 years.

Step 2

The formula to find the required probability is,

\(\displaystyle{P}{\left({X}\leq{6}\right)}={\frac{{{x}-{a}}}{{{b}-{a}}}}\)

Here, a, b stands for lower limit and upper limit.

From the given data, \(\displaystyle{a}={5}\) and \(\displaystyle{b}={7}\)

Now substitute the obtained values in the formula of probability.

\(\displaystyle{P}{\left({X}\leq{6}\right)}={\frac{{{6}-{5}}}{{{7}-{5}}}}\)

\(\displaystyle={\frac{{{1}}}{{{2}}}}\)

\(\displaystyle={0.5}\)

Hence, the probability of randomly chosen student who will stay at most 6 years is 0.5.

Given:

The range of uniform distribution is between 5 to 7 years.

The objective is to find the probability of randomly chosen student who will stay at most 6 years.

Step 2

The formula to find the required probability is,

\(\displaystyle{P}{\left({X}\leq{6}\right)}={\frac{{{x}-{a}}}{{{b}-{a}}}}\)

Here, a, b stands for lower limit and upper limit.

From the given data, \(\displaystyle{a}={5}\) and \(\displaystyle{b}={7}\)

Now substitute the obtained values in the formula of probability.

\(\displaystyle{P}{\left({X}\leq{6}\right)}={\frac{{{6}-{5}}}{{{7}-{5}}}}\)

\(\displaystyle={\frac{{{1}}}{{{2}}}}\)

\(\displaystyle={0.5}\)

Hence, the probability of randomly chosen student who will stay at most 6 years is 0.5.