Suppose the scores on an exam are normally distributed with mean μ = 75 points, and standard deviation σ = 8 points.
The instructor wanted to "pass" anyone who scored above 69. What proportion of exams will have passing scores?
The instructor wanted to "pass" anyone who scored above 69. What proportion of exams will have passing scores?
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z = (X-Mu)/SD
z value corresponding to X=69 is
z = (69-75)/8 = - 0.75
The area under the standard normal curve right to z = - 0.75 indicates the required proportion.
Required proportion = 0.2734 (area between z=-0.75 and the mean) + 0.5000 (total area on the right side of the mean)
= 0.7734 or 77.34%
z value corresponding to X=69 is
z = (69-75)/8 = - 0.75
The area under the standard normal curve right to z = - 0.75 indicates the required proportion.
Required proportion = 0.2734 (area between z=-0.75 and the mean) + 0.5000 (total area on the right side of the mean)
= 0.7734 or 77.34%