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Engineering Statistics ECIV 2305

Engineering Statistics ECIV 2305. 5-2 Linear Combinations of Normal Random Variables. The Distribution of Linear Combinations of Normal Random Variables. Notice that if a = 1/σ and b = −μ/σ, the resulting linear function of X has a standard normal distribution,.

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Engineering Statistics ECIV 2305

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  1. Engineering Statistics ECIV 2305 5-2 Linear Combinations of Normal Random Variables

  2. The Distribution of Linear Combinations of Normal Random Variables

  3. Notice that if a = 1/σ and b = −μ/σ, the resulting linear function of X has a standard normal distribution,

  4. Example 23: Piston Head Construction • Recall that the radius of a piston head X1 has a mean value of 30.00 mm and a standard deviation of 0.05 mm, and that the inside radius of a cylinder X2 has a mean value of 30.25 mm and a standard deviation of 0.06 mm. • What is the mean and the standard deviation of the gap between the piston head and the cylinder? • If the piston head radius and the cylinder radius are taken to be normally distributed, what is the probability that a piston head will not fit within a cylinder? • Suppose that a piston performs optimally when the gap Y is between 0.10mmand 0.35mm. What is the probability that a piston performs optimally?

  5. Example 18 Tomato Plant Heights • Recall that three weeks after planting, the heights of tomato plants have a mean of 29.4 cm and a standard deviation of 2.1 cm. Suppose that 20 tomato plants are planted. • What is the distribution of the average tomato plant height after three weeks of growth?

  6. Example 37 Concrete Block Weights Suppose that a wall is constructed from 24 concrete blocks as illustrated in Figure. What is the distribution of the total weight of the wall?? What is the interval that it gives about a 99.7% chance that the wall has a weight within three standard deviations of its mean value?

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