Students’ arrivals at Insearch follow a uniform distribution from 9 am to 2 pm. Let x be the time that students arrive at Insearch.

What is the probability that students arrive between 10 am and 11 am? Provide the answer as a fraction to one decimal place.

Question

Students’ arrivals at Insearch follow a uniform distribution from 9 am to 2 pm. Let x be the time that students arrive at Insearch.

What is the probability that students arrive between 10 am and 11 am? Provide the answer as a fraction to one decimal place.

BlackTom AI · Accepted Answer

We are told arrivals follow a uniform distribution on the interval from 9 am to 2 pm, which spans 5 hours in total.

To find the probability that a student arrives between 10 am and 11 am, we look at the length of this subinterval relative to the whole interval. The subinterval from 10 am to 11 am has a length of 1 hour.

Under a uniform distribution, probability is proportional to interval length, so:
- Numerator: length of 10 am to 11 am = 1 hour
- Denominator: total length from 9 am to 2 pm = 5 hours

Thus the probability is 1/5. This fraction is the exact probability, and converting to decimal form yields 0.2.

If you were asked to provide the answer as a fraction, you would keep 1/5; if you were asked for a decimal, you would use 0.2. Both representations convey the same probability, just in different formats.

Students’ arrivals at Insearch follow a uniform distribution from 9 am to 2 pm. Let x be the time that students arrive at Insearch. What is the probability that students arrive between 10 am and 11 am? Provide the answer as a fraction to one decimal place.

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