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Answer:
a.) The mean of the six layered plywood is 30 mm
The standard deviation is 0.49 mm
b.) That the thickness is less than 28 mm has a probability of 0.000022.
Step-by-step explanation:
There are six layers in a plywood that is considered. It is also given that the layers are independent and normally distributed.
The thickness of the layers of the plywood have a mean, = 5 mm
and a standard deviation, = 0.2 mm.
a.) Therefore the mean of the six layered plywood is = 6
= 6 × 5 mmm
= 30 mm
The standard deviation of the six layered plywood = =
= 0.49 mm
b.) We are given to find that the probability of the plywood is less than 28 mm thick.
P( thickness < 28 mm)
P( Z < ) = P(Z <
) ⇒ P( Z < -4.082) = 0.000022