Answer:
92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation(which is the square root of the variance)
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
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:
Probability that a year has rainfall of more than 50 inches.
pvalue of Z when X = 50. So
has a pvalue of 0.9319
1 - 0.9319 = 0.0681
Find the probability that out of 15 years, at most 2 have rainfall of more than 50 inches.
This is when
. So
92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.