Solve the problem The systolic blood pressures of the patien

Solve the problem. The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136mm Hg and a standard deviation of 13.8mm Hg Find the two blood pressures having these properties: the mean is midway between them and 90% of all blood pressures are between them. 118.3 mm Hg, 153.7 mm Hg 123.6 mm Hg, 148.4 mm Hg 113.3 mm Hg, 158.7 mm Hg 114.3 mm Hg, 159.7 mm Hg

Solution

Here, we are looking for the 5th and 95th percentile.

for the 5th percentile:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.05      
          
Then, using table or technology,          
          
z =    -1.644853627      
          
As x = u + z * s,          
          
where          
          
u = mean =    136      
z = the critical z score =    -1.644853627      
s = standard deviation =    13.8      
          
Then          
          
x = critical value =    113.3 [ANSWER]

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95th percentile:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.95      
          
Then, using table or technology,          
          
z =    1.644853627      
          
As x = u + z * s,          
          
where          
          
u = mean =    136      
z = the critical z score =    1.644853627      
s = standard deviation =    13.8      
          
Then          
          
x = critical value =    158.7   [ANSWER]  
      
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THUS, THE ANSWERS ARE 113.3 AND 158.7 [ANSWER]