In part (c) we found P(r ≥ 3) = 0.942. Use this value to calculate P(r ≤ 2).P(r ≤ 2)  =  1 − P(r ≥ 3) =  1 −

Use the binomial probability distribution table to find each of the needed probabilities. Then use the probabilities to find the final answer, correct to three decimal places.P(r  ≥  3)  =  P(3) + P(4) + P(5) =

To use the given table, find the section where the left-hand column represents n = 5. Move across the table to the column for p = 0.70.P(r ≥ 3)  =  P(3) + P(4) + P(5) =  0.309 + 0.360 +

Let X be a discrete random variable with the following PMFfor x=oPX(x) = for x=1for x=20 otherwise(a) Find RX, the range of the random variable X.(b) Find P(X ≥ 1.5).(c) Find P(0 < X < 2).(d) Find P(X = 0|X < 2)

Let X be a discrete random variable with the following PMF:PX (x) =0.1 for x = 0.20.2 for x = 0.40.2 for x = 0.50.3 for x = 0.80.2 for x = 10 otherwise(a) Find RX , the range of the random variable X.(b) Find P (X ≤ 0.5).(c) Find P (0.25 < X < 0.75).(d) Find P (X = 0.2 | X < 0.6).

A random variable X has a normal probability distribution N (0, 1). De-termine the value of c as a function of u and o such thatP (X ≥ c) = 9P (X < c).(a) Find the value of c.(b) Evaluate P ((X − µ)2 ≥ σ)