Solve the following problem:
Q1. Find the following values by using the Poisson tables
a. P (x = 6|lamda = 3.8)
b. P (x > 7|lamda = 2.9)
c. P (3 <= x <= 9|lamda = 4.2)
d. P (x = 0|lamda = 1.9)
e. P (x <= 6|lamda = 2.9)
f. P (5 < x <= 8|lamda = 5.7)
Q2. According to the United National Environmental Program and World Health Organization, in Mumbai, India, air pollution standards for particulate matter are exceeded an average of 5.6 days in every three-week period. Assume that the distribution of number of days exceeding the standards per three-week period is Poisson distributed.
a. What is the probability that the standard is not exceeded on any day during a three-week period?
b. What is the probability that the standard is exceeded exactly six days of a three-week period?
c. What is the probability that the standard is exceeded 15 or more days during a three-week period? If this outcome actually occurred, what might you conclude?
Q3. x is uniformly distributed over a range of values from 8 to 21.
a. What is the value of f (x) for this distribution?
b. Determine the mean and standard deviation of this distribution.
c. Probability of (10 less than or equal to x which is less than 17)
d. Probability of (x is less than 22)??
e. Probability of (x is greater than or equal to 7)?