Question

Because not all airline passengers show up for their reserved seat, an airline sells 75 tickets for a flight that holds only 72 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. What is the probability that more than 72 passengers will show up? What are the mean and standard deviation of the number of passengers who show up?

Answer 1

Anyone know how do to do this?

Answer 2

yes

Answer 3

your problem follows a binomial distribution.

Answer 4

could you possibly do that out? i got an answer of .9582 for p and a mean of 67.5 and a std of 2.598 i just want to verify those answers

Answer 5

I get the same mean as you, but that is it.

Answer 6

okay, how did u do the rest? and what did u get?

Answer 7

P(more than 72 passengers will show up)
=P(73 or 74 or 75 passengers show up)
=P(73 passengers show up)+P(74 passengers show up)+P(75 passengers show up)

Answer 8

\[=\sum_{k=73}^{75}{75\choose k}(.9)^k(.1)^{75-k}\]

Answer 9

\[\approx 0.016128757292\]

Answer 10

would the method you used, be used in an entry level stats class?

Answer 11

I don't see why not.

Answer 12

The method i used was p(z<= (x-u)/(up))

Answer 13

most intro stat classes go over the binomial distribution (including the density function)

Answer 14

you are doing a normal approximation?

Answer 15

i guess, i dont really know

Answer 16

for this problem we have n=75 and p=.9 so our mean is 75*.9=67.5 and the sd is

\[\sigma=\sqrt{np(1-p)}=\sqrt{75\cdot.9\cdot.1}=2.598\] so i will agree with you there

Answer 17

have you done any continuity corrections in class?

Answer 18

or do you not know what I am talking about

Answer 19

we have not

Answer 20

if you don't use a continuity correction you should get .041632219204

(approx 1 minus the answer you gave above)

Answer 21

did you compute P(Z>1.732)?

Answer 22

Thats where i went wrong. i used the wrong symbol

Answer 23

Thanks for your help!

Answer 24

np

Answer 25

do you have time for another problem?

Answer 26

maybe

Answer 27

Supposed the contamination particle size (in micrometers) can be modeled as f(x)=3x^-4 for x>1 and f(x)=0 and for x\[\le\]1

Answer 28

a) confirm that f(x) is a probability density function
b) give the cumulative distribution function
c)determine the mean
d) what is the probability that the size of a random particle will be less than 5 micrometers?

Answer 29

I assume you know some calculus.

Answer 30

yes

Answer 31

you need to show that \[\int\limits_{1}^{\infty}3x^{-4}dx=1\]

Answer 32

i have some answers, but i have to sign off. if you could answer this i would greatly appreciate it!

Answer 33

CDF
\[F(x)=\left\{\begin{matrix}0 & \text{if }x<1 \\ \frac{x^3-1}{x^3} & x\ge1\end{matrix}\right.\]

Answer 34

mean is 3/2

Answer 35

prob less than 5 is \[\frac{124}{125}\]