Probability Calculations and Z-Score Analysis in Normal Distributions

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Probability Calculations and Z - Score Analysis in Normal Distributions 1. Find the following probabilities based on a standard normal variable Z . Use Table 1 . (Round your answers to 4 decimal places.) a. P ( Z > 0.74) 0.2296 b. P ( Z ≤ − 1.92) 0.0274 c. P (0 ≤ Z ≤ 1.62) 0.4474 d. P ( − 0.90 ≤ Z ≤ 2.94) 0.8143 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) 0.58 b. P ( X > 20) 0.34 c. P (10 < X < 20) 0.24 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) 0.0446 b. Find P (80 ≤ X ≤ 100). (Round " z " value to 2 decimal places and final answer to 4 decimal places.) P (80 ≤ X ≤ 100) 0.1359 c. Find x such that P ( X ≤ x ) = 0.40. (Round " z " value to 2 decimal places and final answer to nearest whole number.) x 115 d. Find x such that P ( X > x ) = 0.90. (Round " z " value to 2 decimal places and final answer to 1 decimal place.) x 94.4
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