A very reliable baseball player is known to get a hit when at bat 43% of the time.
He is expected to have 102 more times at bat before the end of the season, and he is 48 hits away from breaking a league hitting record.
What is the probability of him breaking that record before the end of the season?
This is a binomial probability with n=102 trials
with probability of 1 hit in 1 trial is p=0.43
we want to find P(x>=48)
Using a TI-84,
1-binomcdf(102,.43,47)
Answer: .2327171125
Or if you have to use tables and the normal approximation, find the
z-score of 47.5, with m=np=(102)(.43) = 43.86 and s=√np(1-p)=√(102)(.43)(1-.43) = 5.00002, use 5
z = (x - m)/s
z = (47.5-43.86)/5 = 3.64/5 = .728
There are two kinds of tables
Look in the table for 0.73 and
if you find in your table that the area to the left of
0.73 is 0.7673, then you subtract from 1 and get .2327.
or
if you find that the area between 0 and 0.73 is 0.2673,
then you subtract from .5000 and get .2327.
Edwin