A certain type of plywood consists of 5 layers. The thickness of the layers follows a normal distribution with mean 5 mm and standard deviation 0.2 mm. Find the probability that the plywood is less than 24mm thick.

Answer: p = 0.01255

Step-by-step explanation: the number of layers (n) = sample size = 5

u = population mean = 5mm,

Population standard deviation = σ = 0.2mm,

x = sample mean = 4.8mm

If the plywood is assumed to be 24mm thick, then the thickness of each layers = 24/5 = 4.8.

Since population standard deviation is known, z test is used in getting the probability that the plywood is less than 24mm thick (p (x< 4.8)).

Z = x - u / (σ/√n)

Z = 4.8 - 5 / (0.2/√5)

Z = - 0.2 / 0.0894427

Z = - 2.24

By using standard normal distribution table whose area is left to the distribution, we have that

Z = 0.01255.

Hence the probability that the plywood is less than 24mm thick is 0.01255