Probability Calculations and Z-Score Analysis in Normal Distributions

An assignment on probability theory, covering Z-score calculations and normal distributions.

Aiden Campbell

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Probability Calculations and Z-Score Analysis in Normal Distributions1.Find the following probabilities based on a standard normal variableZ. UseTable 1.(Round youranswers to 4 decimal places.)a.P(Z> 0.74)0.2296b.P(Z≤−1.92)0.0274c.P(0≤Z≤1.62)0.4474d.P(−0.90≤Z≤2.94)0.81432.The cumulative probabilities for a continuous random variableXareP(X≤10) = 0.42 andP(X≤20) = 0.66. Calculate the following probabilities.(Round your answers to 2 decimal places.)a.P(X> 10)0.58b.P(X> 20)0.34c.P(10 <X< 20)0.243.LetXbe normally distributed with meanμ=120 and standard deviationσ=20. UseTable 1.a.FindP(X≤86).(Round "z" value to 2 decimal places and final answer to 4 decimal places.)P(X≤86)0.0446b.FindP(80≤X≤100).(Round "z" value to 2 decimal places and final answer to 4 decimalplaces.)P(80≤X≤100)0.1359c.Findxsuch thatP(X≤x) = 0.40.(Round "z" value to 2 decimal places and final answer tonearest whole number.)x115d.Findxsuch thatP(X >x) = 0.90.(Round "z" value to 2 decimal places and final answer to 1decimal place.)x94.4

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