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:

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m

it is a. 4.2 because 7.6-3.4 gets the remaining length of 4.2. i might be wrong but i am pretty sure this is the answer.