Answer:
Step-by-step explanation:a.-
a-Notice that this is a binomial probability distribution problem that is generally expressed as:
Given that p=0.45, n=10, the probability of exactly 3 intoxicated drivers is:
Hence, the probability of exactly three intoxicated drivers is 0.1665
ii. The probability of at least 3 intoxicated drivers:
We use the value of p=0.45 and n=10 and (1-p)=0.55:
Hence, the probability off at least three intoxicated drivers is 0.9005
iii. The probability of at most three intoxicated drivers:
-This is calculated the probabilities of between 0 to 3 as:
Hence, the probability off at most three intoxicated drivers 0.0995
b. The probability of between tow and four, inclusive, is calculated by summing the exact probabilities of x=2,3 and x=4:
Hence, the probability of between 2 and 4 is 0.4812
c. The mean of the binomial random variable is calculated as:
Hence, the mean of random variable Y is 4.5
d.Given that n=10 and p=0.45, the standard deviation of the binomial random variable Y is calculated as:
Hence, the standard deviation of the random variable Y is 1.5732