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# Continuous Probability Distributions The data records the length of stay of engineering students in the university. We will assume a uniform distribution between 5 to 7 years, inclusive. What is the probability that a randomly chosen engineering student will stay at most 6 years?

Modeling data distributions
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asked 2021-08-08
Continuous Probability Distributions
The data records the length of stay of engineering students in the university. We will assume a uniform distribution between 5 to 7 years, inclusive. What is the probability that a randomly chosen engineering student will stay at most 6 years?

## Expert Answers (1)

2021-08-08
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.

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