A certain type of stainless steel powder is supposed to have a mean particle diameter of μ = 15 μm. A random sample of 87 particles had a mean diameter of 15.2 μm, with a standard deviation of 1.8 μm. A test is made of H₀ :μ = 15 versus H₁ :μ ≠ 15.

a. Find the P-value.

b. Do you believe it is plausible that the mean diameter is 15 μm, or are you convinced that it differs from 15 μm? Explain your reasoning.