Answer:
a) 0.0202
b)The seller's claim is not correct.
c) If the seller's claim is true we cannot have individual length of 72.15 inch.
Step-by-step explanation:
In the question it is given that
population mean, μ = 72 inch
Population standard deviation, σ = 0.5 inch
Sample size, n = 47
Sample mean, x =72.15 inch
a) z score = =
= 2.0567
P(x ≥ 72.15) = P(z ≥ 2.0567) = 0.5 - 0.4798 = 0.0202
We calculated the probability with the help of standard normal table.
b) The sellers claim that the machine cuts the lumber with a mean length of 72 inch is not correct as we obtained a very low probability.
c)If we assume that the seller's claim is true that is the machine cuts the lumber into mean length of 72 inch then we cannot have an individual length 72.15.
Standard error = = 0.0729
Because it does not lie within the range of two standard errors that is (μ±2 standard error) = (71.8541,72.1458)