The situation represents a binomial probabilty with the probability of success (p) = 47% or 0.47 and the number of trials (n) = 10.
The probability of a binomial distribution is given by:
Part A:
<span>The probability that the number who consider themselves baseball fans is exactly five is given by:
Part B:
</span>The probability that the number who consider themselves baseball fans is at least six is given by:
This can be approximated using normal distribution as I will illustrate in part c.
Part C:
The probability that the number who consider themselves baseball fans is less than four is given by:
We can approximate this using normal distribution by subtracting 0.5 from the least value and adding 0.5 to the greatest value.
This gives
The mean of a binomial distribution is given by
, while the standard deviation is given by
.
Thus,
The probability of a nomal distribution between two values (a, b) is given by:
Thus,