A regression analysis was completed for y = 28-day standard-cured strength (psi)

Question

A regression analysis was completed for y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = 1200 + 1-2x. The standard deviation of random errors is 300 psi. What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2500? What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2400?

Explanation / Answer

(a)

Given equation:
y' = 1200 + 1.2x

At x = 2500, y = 1200 + 1.2(2500) = 4200

Calculating z-score: z = (5000-4200)/300 = 2.67

Looking from the z-table, required probability is:

P(y > 5000) = P(z > 2.67) = 1 - P(z<2.67) = 1-0.9962 = 0.0038

(b)

At x = 2400, y = 1200 + 1.2(2400) = 4080

Calculating z-score: z = (5000-4080)/300 = 3.06

Looking from the z-table, required probability is:

P(y > 5000) = P(z > 3.06) = 1 - P(z<3.06) = 1-0.9988 = 0.0012

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