Answer:
4.23% probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill.
Step-by-step explanation:
For each installation, there are only two possible outcomes. Either it reduces the utility bill, or it does not. The probabilities for each installation reducing the utility bill are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
Solar-heat installations successfully reduce the utility bill 60% of the time, which means that
What is the probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill?
This is when
. So
In which
So
4.23% probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill.