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Serga [27]
3 years ago
6

Every time you have your cholesterol measured, the measurement may be slightly different due to random fluctuations and measurem

ent error. Suppose that for you, the population of possible cholesterol measurements if you are healthy has a mean of 190 and a standard deviation of 10. Further, suppose you know you should get concerned if your measurement ever gets up to the 97th percentile. What level of cholesterol does that represent?
Mathematics
1 answer:
zmey [24]3 years ago
7 0

Complete Question

The complete question is shown on the first uploaded image

Answer:

a i

P(X  < 185 ) =  0.3085

a ii

P(X  > 195 ) =  0.3085

a iii

P(185 < X <  195 ) = 0.3829

b

x =  208.8

Step-by-step explanation:

From the question we are told that  

   The mean is  \mu =  190

   The standard deviation is  \sigma  =  10

   

Generally the probability is  less than 185  is mathematically represented as

      P(X  < 185 ) =  P(\frac{X - \mu }{\sigma } < \frac{185 - 190 }{10 }   )

Generally \frac{X - \mu }{\sigma } = Z (The  \ standardized \  value  \  \ of  \  X)

=>   P(X  < 185 ) =  P(Z< -0.5)

From the z-table the p value  of  (Z< -0.5) is

    P(Z< -0.5) = 0.3085

So

    P(X  < 185 ) =  0.3085

Generally the probability is  less than 185  is mathematically represented as

      P(X > 195 ) =  P(\frac{X - \mu }{\sigma } > \frac{195 - 190 }{10 }   )

=>   P(X  >  195 ) =  P(Z > 0.5)

From the z-table the p value  of  (Z > 0.5) is

    P(Z > 0.5) = 0.3085

So

    P(X  > 195 ) =  0.3085

Generally the probability is  less than 185  is mathematically represented as

      P(185 < X <  195 ) =  P( \frac{185 - 190 }{10 } <  \frac{X - \mu }{\sigma } <  \frac{195 - 190 }{10 } )

=>   P(185 < X <  195 ) =  P(-0.5 < Z > 0.5)

=>   P(185 < X <  195 ) = P(Z  <  0.5 ) -  P(Z <  -0.5)

From the z-table the p value  (Z <  0.5) and  (Z <  -0.5) is  

    P(Z < 0.5) =  0.6915

and  

   P(Z < - 0.5) = 0.3085

So

=>   P(185 < X <  195 ) = 0.6915 -  0.3085

=>   P(185 < X <  195 ) = 0.3829

Generally the level of cholesterol the 97th percentile represents  is mathematically evaluated as

    P(X < x ) =  0.97

=> P(X < x ) = P(\frac{X - \mu}{\sigma }  <  \frac{x - 190}{10 }  ) = 0.97

=>   P(X < x ) = P(Z <  \frac{x - 190}{10 }  ) = 0.97

From the z-table  the z-score for  0.97  is  

      z-score =  1.88

=>

  \frac{x - 190}{10 } =  1.88

=>x =  208.8

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