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FIND THE FOLLOWING PROBABILITIES BASED ON A STANDARD NORMAL VARIABLE Z

FIND THE FOLLOWING PROBABILITIES BASED ON A STANDARD NORMAL VARIABLE Z

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Author: Christine Farr
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1. Find the following probabilities based on a standard normal variable Z. Use Table 1. (Round youranswers to 4 decimal places.)a.b.c.d.P(Z > 0.74)P(Z ≤ −1.92)P(0 ≤ Z ≤ 1.62)P(−0.90 ≤ Z ≤ 2.94)2. The cumulative probabilities for a continuous random variable X are P(X ≤ 10) = 0.42 and P(X ≤20) = 0.66. Calculate the following probabilities. (Round your answers to 2 decimal places.)a. P(X > 10)b. P(X > 20)c. P(10 < X < 20)3. Let X be normally distributed with mean μ = 120 and standard deviation σ = 20. Use Table 1.a. Find P(X ≤ 86). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)P(X ≤ 86)b. Find P(80 ≤ X ≤ 100). (Round "z" value to 2 decimal places and final answer to 4 decimalplaces.)P(80 ≤ X ≤ 100)c. Find x such that P(X ≤ x) = 0.40. (Round "z" value to 2 decimal places and final answer tonearest whole number.)xd. Find x such that P(X > x) = 0.90. (Round "z" value to 2 decimal places and final answer to 1decimal place.)x4. Let X be normally distributed with mean μ = 2.5 and standard deviation σ = 2. Use Table 1.a. Find P(X > 7.6). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)P(X > 7.6)b. Find P(7.4 ≤ X ≤ 10.6). (Round "z" value to 2 decimal places and final answer to 4 decimalplaces.)P(7.4 ≤ X ≤ 10.6)c. Find x such that P(X > x) = 0.025. (Round "z" value and final answer to 2 decimal places.)xd. Find x such that P(x ≤ X ≤ 2.5) = 0.4943. (Negative value should be indicated by a minus sign.Round "z" value and final answer to 2 decimal places.)x5. Find the following z values for the standard normal variable Z. Use Table 1. (Negative valuesshould be indicated by a minus sign. Round your answers to 2 decimal places.)a.b.c.d.P(Z ≤ z) = 0.9744P(Z > z) = 0.8389P(−z ≤ Z ≤ z) = 0.95P(0 ≤ Z ≤ z) = 0.3315

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