An industrial oven used to cure sand cores for a factory manufacturing engine bl
ID: 3177729 • Letter: A
Question
An industrial oven used to cure sand cores for a factory manufacturing engine blocks for small cars is able to maintain fairly constant temperatures. The temperature range of the oven follows a normal distribution with a mean of 483F and a standard deviation of 21F. Leslie Larsen, president of the factory, is concerned about the large number of defective cores that have been produced in the past several months. If the oven gets hotter than 500 F the core is defective. What is the probability that the oven will cause a core to be defective? What is the probability that the temperature of the oven will range from 495F to 510F?
Please show your work, if possible use excel formulas
Explanation / Answer
Mean ( u ) =483
Standard Deviation ( sd )=21
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P(X > 500) = (500-483)/21
= 17/21 = 0.8095
= P ( Z >0.81) From Standard Normal Table
= 0.2091
probability that the oven will cause a core to be defective is 20.91%
b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 495) = (495-483)/21
= 12/21 = 0.5714
= P ( Z <0.5714) From Standard Normal Table
= 0.71615
P(X < 510) = (510-483)/21
= 27/21 = 1.2857
= P ( Z <1.2857) From Standard Normal Table
= 0.90073
P(495 < X < 510) = 0.90073-0.71615 = 0.1846