Problem 5E

In a lab experiment involving inorganic syntheses of molecular precursors to organometallic ceramics, the final step of a five-step reaction involves the formation of a metal–metal bond. The probability of such a bond forming is p = 0.20. Let X equal the number of successful reactions out of n = 25 such experiments.

(a) Find the probability that X is at most 4.

(b) Find the probability that X is at least 5.

(c) Find the probability that X is equal to 6.

(d) Give the mean, variance, and standard deviation of X.

Answer

Step 1 of 5

Here n=25,

p=0.2,

q=0.8

X~B(25,0.2)

The pmf of binomial distribution is P(x)=ncx px qn-x ,x=1,2,3,....n