A recent study showed that 75 % of commercial airline flights in and out of the US airports were on-time arrivals and 19 % were late departures. three hundred flights are to be randomly identified from all flights and their flight logs examines closely.
What is the probability that more then 80 percent of the sample will be on-time arrival
This is a binomial probablity, where
,
= 80% of 300 =
If , then this is approximately normally
distributed. , so
the normal approximation will be close.
Since we read the words "more then 80 percent", we do not
include the 240 bar of the implied histogram, the base of
which goes from 239.5 to 240.5. So the first bar of the
histogram we include starts at 240.5. So we take that value
for x:
, rounded to
nearest hundredth.
Now we need to find out the area under the normal curve
to the right of the black vertical line at 2.07
Normal tables are set up to give the area between the y-axis and
that black line drawn at .
So we look down the left column, till we see 2.0,then across the top
to the hundredth digit, which is .07, so we read .4808. Since all the
area to the right of the y-axis is .5, we subtract .5-.4808 and
get .0192.
Edwin