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Suppose the force acting on a column that helps to support a building is a normally...

Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 18.0 kips and standard deviation 1.50 kips. Compute the following probabilities by standardizing and then using a standard normal curve table from the Appendix Tables. (Round your answers to four decimal places.) (a) P(X ≤ 18) (b) P(X ≤ 19.5) (c) P(X ≥ 12) (d) P(17 ≤ X ≤ 21) (e) P(|X − 18| ≤ 1)

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(a) P(X 18) Normal Distribution, μ 18, σ 1.5 Since this is continuous distribution, P(X 18) P(X< 18) Since Normal distribution is symmteric, the probability of getting a value below the mean is equal to probability of getting value above the mean, and is equal to 2 P(X < 18)= 0.5 50% We can solve this using z-values as follows: we convert this to standard normal using z = 18 (18) 1.5 0.00 P(Z <0.00) Area to the left of 0.00 5000 0.00 P(X < 18)-P(Z < 0.00)-0.5000 (from z-table) P(Z < 0): in a z-table having area to the left of z, locate O in the left most column. Move across the row to the right under column 0.00 and get value 0.5000 Using technology, ansver is: 0.50000000000000

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