Question

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 15% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.) (a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip? (b) If six reservations are made, what is the expected number of available places when the limousine departs? places (c) Suppose the probability distribution of the number of reservations made is given in the accompanying table. Number of reservations 3 4 5 6 Probability 0.11 0.19 0.29 0.41 Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X. x 0 1 2 3 4 p(x)

          An airport limousine can accommodate up to four passengers on
any one trip. The company will accept a maximum of six reservations
for a trip, and a passenger must have a reservation. From previous
records, 15% of all those making reservations do not
appear for the trip. Answer the following questions, assuming
independence wherever appropriate. (Round your answers to three
decimal places.)
(a) If six reservations are made, what is the probability that
at least one individual with a reservation cannot be accommodated
on the trip?
(b) If six reservations are made, what is the expected number of
available places when the limousine departs?
 places
(c) Suppose the probability distribution of the number of
reservations made is given in the accompanying table.
Number of reservations    
3
4
5
6
Probability
    0.11    
    0.19    
    0.29    
    0.41    
Let X denote the number of passengers on a
randomly selected trip. Obtain the probability mass function
of X.
x
0
1
2
3
4
p(x)

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Added by Walter S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Juan Nicolás

02/17/2022

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Step 1: Calculate the probability that at least one individual with a reservation cannot be accommodated on the trip when six reservations are made. Show more…

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An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 15% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.) (a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip? (b) If six reservations are made, what is the expected number of available places when the limousine departs? places (c) Suppose the probability distribution of the number of reservations made is given in the accompanying table. Number of reservations 3 4 5 6 Probability 0.11 0.19 0.29 0.41 Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X. x 0 1 2 3 4 p(x)

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Transcript

00:01 Hello, so today i'm going to answer your question out the probability of having a limousine cramp using the binomial distribution.

00:08 So the binomial distribution is when you want to find the probability of an specific event or the number of specific events with this formula.

00:17 So n would be a number of trials or the number of reservations that individuals made, x, the specific amount of passengers that would appear, and piece the probability of a single success or the probability that the individuals appear.

00:28 So first, what is the probability that x is rated than for or that at least when you are the number of the passengers that will appear? individual don't have seat so that there are 5 or 6 reservations.

00:34 So basically i just use this formula.

00:38 So for example in the case of 5 is 6, n minus x will be 1 factorial x 5 factorial, relative of a single success 0 .75 raise to 5 and 0 .15 raise to 1.

00:49 Then i repeat the same process for 1 and the addition of those is 0 .534 so the probability that at least one individual don't have a seat is 0 .534 if there were 6 reservations made.

01:00 Then what is the expected number you need to take the probability and multiply it by n so 0 .75 times 6 this give you 4 .5 it's important that you understand because it's not possible to have a decimal person like to have half person then i would run the to 5 and then they ask you to calculate the much function so i just need to apply the same formula for 0 1 2 3 and 4 so for example for the case will 0 will be 6 factorial over 6 factorial times 0 factorial so this will be 1 this will be 1 this will be 1 because as you may recall from your algebra classes, every number raised to zero would be one.

01:39 And then this value is 0 .00 and so on, but because you need to run it to three decimal places, it's just zero...

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