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aeviyons
18.02.2020 •
Mathematics
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.
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Ответ:
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
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