What is the probability that in 120 tosses of a fair coin between 40% and 60% (inclusively) will be heads?
Use the normal approximation to the Binomial distribution for this.Originally Posted by swoopesjr01
The mean number of heads is , the standard deviation is
Between 40% and 60% of 120 is between 48 and 72. To allow for the
fact that we can only have an integer number of heads we work the
normal approximation (which is continuous) for between 47.5 and 72,5
heads.
The z-scores for the ends of the range are:
Now looking the probability of a standard normal random variable having
a value in the range we find the probability is
.
This last answer may be compared with PH's calculation based on using
the exact binomial formula.
RonL