A Stat 311 HW #5.pdf - Homework#5 u2013 Chapter3 11(20pts...

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Homework #5 Chapter3 & 11 (20pts for turned in on time) 1. (10pts, 0.5 point each)Practice on using standard normal table. Keep in mind the probability given in the table always represent the area to the LEFT of the z-score. (1) Find the probability for the following event: ( Z table only covers z-scores between -3.49 and 3.49, by a step of 0.01. But in reality, z-score can be any real numbers. If you need to evaluate a probability with z score outside of the z table, use the closest z score to approximate.) a) P (z < 1.22) b) P (z < - 1.22) c) P (z < -5) d) P(z < 5) e) P (z > 0.68) f) P (z > -0.68) g) P(z > 5) h) P(z > -5) i) P(0.52 < z < 1.24) j) P(-0.52 < z < 1.24) (2) Find the z-score 𝑧 0 for the following event: ( If you cannot find the exact probability value on the z table, use the closest value to approximate) k) P (z < 𝑧 0 ) = 0.0618 l) P (z < 𝑧 0 ) = 0.1423 m) P (z < 𝑧 0 ) = 0.8997 n) P(z < 𝑧 0 ) = 0.9505 o) P (z > 𝑧 0 ) = 0.0618 p) P (z > 𝑧 0 ) = 0.1423 q) P(z > 𝑧 0 ) = 0.8997 r) P(z > 𝑧 0 ) = 0.9505 s) P(z < 𝑧 0 ) = 0.03 t) P(z > 𝑧 0 ) = 0.98
Homework #5 Chapter3 & 11 (20pts for turned in on time) 2. (6 points) For the 68-95-99.7 rule, the number is approximation. Look up the normal table, and find the exact probability of within 1 σ of μ, within 2 σ of μ, and within 3 σ of μ for any normal distribution N (μ, σ ). For example, the 68% rule states that the probability within 1 σ of µ is 68%. It is like stating P(-1 < z < +1) = 0.68. What would the standard normal table give you in terms of these probabilities? Complete the table below. From 68-95-99.7 rule (Approximation) From Z table (Accurate) Differences P ( -1 < z < 1) 0.68 P(-2 < z < 2) 0.95 P(-3 < z < 3) 0.997 3. (20 points, 2 points each)To find the probability for any normal distribution, you will have to standardize the normal variable X to standard normal variable Z before you can use the normal table to look up the probabilities. And the standardization is through Z =
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