Suppose a movie starts at 5:00 p. m. and Lindsay, a customer who is always late, arrives at the movie theater at a random time between 5:10 p. m. and 5:45 p. m. Lindsay's late arrival time, in minutes, represented by X, models a uniform distribution between 10 and 45 min. Determine the height of the uniform density curve. Provide your answer with precision to three decimal places.

height= ?

Calculate the probability that Lindsay is late by 20 min or less, P(X?20). Provide your answer with precision to three decimal places.

P(X?20) = ?

a) We know that the distribution for X is given by:

The density function for this distirbution is given by:

So then the height of the uniform density curve would be given by:

b) For this case we want to calculate the following probability:

And we can use the cumulative distribution function given by:

And we can calculate the probability like this:

Step-by-step explanation:

For this case we define our random variable X="Lindsay's late arrival time, in minutes"

Part a

We know that the distribution for X is given by:

The density function for this distirbution is given by:

So then the height of the uniform density curve would be given by:

Part b

For this case we want to calculate the following probability:

And we can use the cumulative distribution function given by:

And we can calculate the probability like this:

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step-by-step explanation:

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