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julia-pushkina [17]
3 years ago
9

2. The mean birth weight of a full term boy born in the US is 7.7 lbs, with standard deviation of 1.1 lbs. A. Find the probabili

ty that a boy born full term in the US weighs less than 7 lbs. B. Find the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs.
Mathematics
1 answer:
Fed [463]3 years ago
4 0

Answer:

A

The value is P( X  <  7 ) =0.26226

B

The value is P( X  <  7 ) = 0.00073

Step-by-step explanation:

From the question we are told that

  The population mean is  \mu = 7.7 lbs

   The standard deviation is \sigma  = 1.1 \ lbs

  The sample size is  n =  25

Generally the probability that a boy born full term in the US weighs less than 7 lbs is mathematically represented as

     P( X  <  7 ) =  P( \frac{X - \mu }{\sigma}  <  \frac{7 - 7.7 }{1.1 } )

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

=>   P( X  <  7 ) =  P(Z

From the z table  the area under the normal curve to the left corresponding to    -0.6364  is

    P(Z

=>   P( X  <  7 ) =0.26226

Generally the standard error of mean is mathematically represented as  

       \sigma_{x} = \frac{\sigma }{\sqrt{n} }

=>     \sigma_{x} = \frac{ 1.1  }{\sqrt{25} }

=>     \sigma_{x} = 0.22

Generally the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs is mathematically represented as

         P( \= X  <  7 ) =  P( \frac{\= X - \mu }{\sigma_{x}}  <  \frac{7 - 7.7 }{ 0.22 } )

=>      P( X  <  7 ) =  P(Z

From the z table  the area under the normal curve to the left corresponding to    -3.1818  is

=>      P(Z

=>      P( X  <  7 ) = 0.00073

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