The MBA program at Harvard has found over the past 20 years that the proportion

Question

The MBA program at Harvard has found over the past 20 years that the proportion of accepted students who do not enroll has been in statistical control with an average of 0.030. Assuming the most recent class had 400 acceptances, what would be the Shewhart limits used to determine if the enrollment rate is unusually low or high? (Round to 3 digits.)

A)UCL = 0.144, LCL = 0.084

B)UCL=0.144, LCL = 0.000

C)UCL = 0.054, LCL = -0.084

D)UCL=.056, LCL=.004

E)None of the above

A)UCL = 0.144, LCL = 0.084

B)UCL=0.144, LCL = 0.000

C)UCL = 0.054, LCL = -0.084

D)UCL=.056, LCL=.004

E)None of the above

Explanation / Answer

Sample size (N) = 400

p_bar = 0.030

Std. Error = Sp = SQRT(p_bar*(1 - p_bar) / N) = SQRT(0.03*(1 - 0.03)/400) = 0.0085

3-sigma conrol limts are:

UCL = p_bar + 3 * Sp = 0.030 + 3*0.0085 = 0.056
LCL = max(0, p_bar - 3 * Sp) = max(0, 0.030 - 3*0.0085) = 0.004

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