# Tutoring on the Normal Distribution

The U.S. Airforce requires that pilots have a height between 64 in. and 72 in. If women’s heights are normally distributed with a mean of 63.8 in. and a standard deviation of 2.25 in, find the percentage of women that meet the height requirement. Show your calculations using Excel functions in the area to the right of this text box and answer the problem with explanations below.

<p> What is the cumulative area from the left under the curve for a z-score of -0.675? What is the area on the right of that z-score? Hint: You will have two answers (one for the left and one for the right). Student’s partially finished answer: The first part is to find the cumulative area from the left under the curve for a z-score of -0.675. This means that I need to find the probability that a z-score is less than -0.675. Show your calculations using Excel functions in the area to the right of this text box and finish answering the problem with explanations below.

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<i> If the area under the standard normal distribution curve is 0.1125 from the right, what is the corresponding z-score?   Student’s incorrect answer: We plug in “=NORM.S.INV(0.1125)” into Excel and get a z-score of -1.21. Identify where the student went wrong when solving the problem above. Show how to correctly calculate the answer using Excel in the area to the right of this text box. Finish the problem by stating how to correctly set up the problem and solve it below.

<p> A research shows that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.422 and a standard deviation of 0.73. Earthquakes with magnitudes less than 2.00 are considered “microearthquakes” that humans do not feel. What percentage of earthquakes fall into this category?   Student’s partially finished answer: We need to find the probability that earthquakes fall into the microearthquake category. The first step is to find the probability that the Richter scale is less than 2.00. Show your calculations using Excel functions in the area to the right of this text box and finish answering the problem with explanations below.