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  A patient is said to be hypokalemic (low potassium in the blood) if the measured level of potassium is 3

2)  A patient is said to be hypokalemic (low potassium in the blood) if the measured level of potassium is 3.5 or less. The units for this measure are meq/l, or miliequivalents per liter.) An individual’s potassium level is not constant, however, but varies from day to day. In addition, the measurement procedure itself has some variation.

(Assume that Judy’s level of potassium follows a normal distribution and use the table of  the standard normal cumulative distribution function that appears below to answer the questions.)

 

MTB > print c1-c2

 

Data Display

 

 Row      z    P[Z<=z]

 

   1   -3.0   0.001350

   2   -2.9   0.001866

   3   -2.8   0.002555

   4   -2.7   0.003467

   5   -2.6   0.004661

   6   -2.5   0.006210

   7   -2.4   0.008198

   8   -2.3   0.010724

   9   -2.2   0.013903

  10   -2.1   0.017864

  11   -2.0   0.022750

  12   -1.9   0.028717

  13   -1.8   0.035930

  14   -1.7   0.044565

  15   -1.6   0.054799

  16   -1.5   0.066807

  17   -1.4   0.080757

  18   -1.3   0.096800

  19   -1.2   0.115070

  20   -1.1   0.135666

  21   -1.0   0.158655

  22   -0.9   0.184060

  23   -0.8   0.211855

  24   -0.7   0.241964

  25   -0.6   0.274253

  26   -0.5   0.308538

  27   -0.4   0.344578

  28   -0.3   0.382089

  29   -0.2   0.420740

  30   -0.1   0.460172

  31    0.0   0.500000

 

a)       Judy has a mean potassium level of 3.8 and a standard deviation on 0.2. If she is measured on many days, on what proportion of days will the measurement suggest that Judy is hypokalemic?

 

b)       Answer the previous question with a value for the standard deviation of 0.3.

 

c)       Peter, another patient, has been tested many times and has been declared hypokalemic  30.85% of the time. If the standard deviation of his measurements is 0.3, determine the mean value of the measurements. Assume a normal distribution.