# SOLUTION: Can anyone help me with this? I need to show my work but not sure what steps I need to take to solve this. X has a normal distribution with a mean of 80.0 and a standard deviati

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Can anyone help me with this? I need to show my work but not sure what steps I need to take to solve this. X has a normal distribution with a mean of 80.0 and a standard deviati      Log On

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 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Probability-and-statistics Question 619302: Can anyone help me with this? I need to show my work but not sure what steps I need to take to solve this. X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities: (A) P(x < 77.0) (B) P(75.0 < x < 85.0) (C) P(x > 85.0)Answer by stanbon(57387)   (Show Source): You can put this solution on YOUR website!X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities: ---- The measuring stick you have to use to find probabilities is the z-chart or technology that you have available. ------------------------------- (A) P(x < 77.0) z(77) = (77-80)/3.5 = -3/3.5 = -0.8571 That simply means 77 is 0.8571 standard deviations below the mean. Now use your z-chart to find the probability to the left of -0.8571 Ans: normalcdf(-100,-0.8571) = 0.1957 -------------------------------------------- (B) P(75.0 < x < 85.0) z(75) = (75-80)/3.5 = -1.4286 z(85) = (85-80)/3.5 = +1.4286 P(75 ================================= (C) P(x > 85.0)= P(z > 1.4286) = normalcdf(1.4286,100) = 0.0766 ================ Cheers, Stan H. ================