In Section 1.4 we saw that each space shuttle has six O-rings and that each O-ring fails with probability where a = 5.085, b = −0.1156, and t is the temperature (in degrees Fahrenheit) at the time of...

In Section 1.4 we saw that each space shuttle has six O-rings and that each O-ring fails with probability

where a = 5.085, b = −0.1156, and t is the temperature (in degrees Fahrenheit) at the time of the launch of the space shuttle. At the time of the fatal launch of the Challenger, t = 31, yielding p(31) = 0.8178.

a. Let X be the number of failing O-rings at launch temperature 31◦F. What type of probability distribution does X have, and what are the values of its parameters?

b. What is the probability P(X ≥ 1) that at least one O-ring fails?