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2. MD Use Tools Marcela gets to school later than her friend Kim about half the time. Describe a way to simulate this event for 10 school days. Then perform the simulation. How many times does it show Marcela arriving later than Kim? What is the experimental probability of this event?

User PeteT
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1 Answer

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We know that "Marcela gets to school later than her friend Kim about half the time", so in a 10-day period, about half of that number of days Marcela is expected to arrive later than Kim. That expected amount of days is 10/2 = 5.

We can describe this as a probabilistic model as:

We have an event that can be decribed as "Marcela arrives later than Kim".

This event happens each day with a probability of around p = 0.5, which is the translation of "about half the time". This means that each day there is a 50% chance that Marcela is late.

Then, this event can be represented as a Bernoulli random variable with p = 0.5.

If we repeat this experiment 10 times (one for each day), we will have a Binomial variable with p=0.5 and n=10.

This will result in a binomial distribution with parameters p=0.5 and n=10 and the following histogram:

Answer:

How many times does it show Marcela arriving later than Kim?

Half the time Marcela will be arriving later than Kim. If we simulate it 10 times, we expect to get a result of 5 days of Marcela arriving later than Kim.

What is the experimental probability of this event?​

The experimental probability comes from the information given: we know that half of the time Marcela arrives later, so this can be translated to a probability of 0.5 (or 50%) of Marcela arriving later than Kim.

2. MD Use Tools Marcela gets to school later than her friend Kim about half the time-example-1
User Gardarvalur
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