Chapter 5.2, Problem 5.31E

Back Pain Six in 10 aduts say lower back pain substantially limits their athletic activities.3 A random sample of $n=8$ adults were asked if lower back pain was a limiting factor in their athletic activities. The printout below shows the cumulative and individual probabilities for a binomial random variable with $n=8$ and $p=\mathrm{.6.}$

1. Use the binomial formula to find the probability that all eight indicate that lower back pain was a limiting factor in their athletic activities.
2. Confirm the results of part a using the printout.
3. What is the probability that at most seven individuals give lower back pain as a limiting factor in their athletic activities?