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As in exercise 3 Cholesterol levels in health us adults average about 215mg/Dl with a Standard...

As in exercise 3 Cholesterol levels in health us adults average about 215mg/Dl with a Standard deviation of about 30 mg /dl and are roughly normally distributed If the cholestrol levels of a sample of 42 healthy us adults is taken what is the probablility that the mean cholesterol level of the sample

A. will be no more than 215?

b. will be between 205 and 225

c. Will be less than 200?

d. Will be greater than 220?

Solutions

Expert Solution

a)

µ =    215                                  
σ =    30                                  
n=   42                                  
                                      
X =   215.00                                  
                                      
Z =   (X - µ )/(σ/√n) = (   215   -   215   ) / (   30   / √   42   ) =   0.000
                                      
P(X ≤   215   ) = P(Z ≤   0.000   ) =   0.5000                  
excel formula for probability from z score is =NORMSDIST(Z)                                      
.....

b)

µ =    215                                  
σ =    30                                  
n=   42                                  
we need to calculate probability for ,                                      
205   ≤ X ≤    225                              
X1 =    205   ,    X2 =   225                      
                                      
Z1 =   (X1 - µ )/(σ/√n) = (   205   -   215   ) / (   30   / √   42   ) =   -2.16
Z2 =   (X2 - µ )/(σ/√n) = (   225   -   215   ) / (   30   / √   42   ) =   2.16
                                      
P (   205   < X <    225   ) =    P (    -2.16   < Z <    2.16   )   
                                      
= P ( Z <    2.16   ) - P ( Z <   -2.16   ) =    0.98462   -    0.01538   =    0.96925  
excel formula for probability from z score is =NORMSDIST(Z)                                      

c)

µ =    215                                  
σ =    30                                  
n=   42                                  
                                      
X =   200.00                                  
                                      
Z =   (X - µ )/(σ/√n) = (   200   -   215   ) / (   30   / √   42   ) =   -3.240
                                      
P(X ≤   200   ) = P(Z ≤   -3.240   ) =   0.0006                  
excel formula for probability from z score is =NORMSDIST(Z)                                      

.

d)

µ =    215                                  
σ =    30                                  
n=   42                                  
                                      
X =   220                                  
                                      
Z =   (X - µ )/(σ/√n) = (   220   -   215   ) / (    30   / √   42   ) =   1.1
                                      
P(X ≥   220   ) = P(Z ≥   1.08   ) =   P ( Z <   -1.080   ) =    0.1400      
excel formula for probability from z score is =NORMSDIST(Z)                                      


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