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Elis [28]
2 years ago
12

Let be a continuous random variable that follows a normal distribution with a mean of and a standard deviation of . Find the val

ue of so that the area under the normal curve to the right of is . Round your answer to two decimal places.
Mathematics
1 answer:
Oksi-84 [34.3K]2 years ago
8 0

Complete Question

Let x be a continuous random variable that follows a normal distribution with a mean of 550 and a standard deviation of 75.

a

Find the value of x so that the area under the normal curve to the left of x is .0250.

b

Find the value of x so that the area under the normal curve to the right ot x is .9345.

Answer:

a

  x  = 403

b

 x  = 436.75

Step-by-step explanation:

From the question we are told that

   The  mean is  \mu = 550

   The standard deviation is  \sigma = 75

Generally the value of x so that the area under the normal curve to the left of x is 0.0250 is mathematically represented as

     P( X <  x) = P( \frac{x - \mu  }{ \sigma}  <  \frac{x - 550 }{75 } ) = 0.0250

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

     P( X <  x) = P( Z < z ) = 0.0250

Generally the critical value of  0.0250 to the left  is  

       z = -1.96

=>    \frac{x- 550 }{75} = -1.96

=>    x  = [-1.96 * 75 ]+ 550      

=>    x  = 403

Generally  the value of x so that the area under the normal curve to the right of x is 0.9345 is mathematically represented as

        P( X <  x) = P( \frac{x - \mu  }{ \sigma}  <  \frac{x - 550 }{75 } ) = 0.9345

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

     P( X <  x) = P( Z < z ) = 0.9345

Generally the critical value of  0.9345 to the right  is  

       z = -1.51

=>    \frac{x- 550 }{75} = -1.51

=>    x  = [-1.51 * 75 ]+ 550      

=>    x  = 436.75

   

     

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