Answer:
(a) P (X = 0) = 0.006
(b) P (X = 1) = 0.0403
(c) P (X ≥ 2) = 0.9537
(d) P (X > 5) = 0.1664
Step-by-step explanation:
Let <em>X</em> = number of successful appeals.
The probability that an appeal is successful is, <em>p</em> = 0.40.
The sample size is, <em>n</em> = 10.
The random variable .
The probability function of a Binomial distribution is:
(a)
The probability that none of the appeals is successful is:
Thus, the probability that none of the appeals is successful is 0.006.
(b)
The probability that exactly one of the appeals will be successful is:
Thus, the probability that exactly one of the appeals will be successful is 0.0403.
(c)
The probability that at least two of the appeals will be successful is:
Thus, the probability that at least two of the appeals will be successful is 0.9537.
(d)
The probability that more than half of the appeals will be successful is:
Thus, the probability that more than half of the appeals will be successful is 0.1664.