Help on finding indicated probability.

slumberdoll · #1 $Old$ November 1st, 2009, 10:06 PM

Hi guys,

I've been having a lot of trouble with this particular problem and I was wondering if I could get some help or insight. I'd greatly appreciate it.

The question is:

An airline estimates that 98% of people booked on their flights actually show up. If the airline books 62 people on a flight for which the maximum number is 60, what is the probability that the number of people who show up will exceed the capacity of the plane?

The answer in the book says it's .6474 but I'm unable to get that answer.

Robb · #2 $Old$ November 1st, 2009, 10:31 PM

Hello,

Probability that it will exceed the capacity is equal to the probability 61 people show up plus the probability that 62 people show up;

$P(\mbox{61 people})=62C1\cdot(.98)^{61}\cdot (.02)^2=.361587$
$P(\mbox{62 people}=62C0\cdot(.98)^{62}=.28577$
so
$P(\mbox{exceed capacity})=.3616+.2858=.6474$

slumberdoll · #3 $Old$ November 2nd, 2009, 09:38 AM

Thank you so much Robb! I realized I had mixed up some of the numbers when I plugged it into the calculator.