Someone claims that a certain suspension contains at least seven particles per mL. You sample 1 mL of solution. Let X be the number of particles in the sample.
a. If the mean number of particles is exactly seven per mL (so that the claim is true, but just barely), what is P(X ≤ 1)?
b. Based on the answer to part (a), if the suspension contains seven particles per mL, would one particle in a 1 mL sample be an unusually small number?
c. If you counted one particle in the sample, would this be convincing evidence that the claim is false? Explain.
d. If the mean number of particles is exactly 7 per mL, what is P(X ≤ 6)?
e. Based on the answer to part (d), if the suspension contains seven particles per mL, would six particles in a 1 mL sample be an unusually small number?
f. If you counted six particles in the sample, would this be convincing evidence that the claim is false? Explain.