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Suppose that the random variable z has a standard normal distribution. Find each of the following z points, and use the normal table to find each z point. (Round z0.03 and –z0.03 to 3 decimal places and other answers to 2 decimal places; Use the closest value of Z when there is not an exact match; if the Zvalues are equidistant, then average the two Z values. Negative values should be indicated by a minus sign.)

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  a.   z0.25 [removed]  
  b.   z0.28 [removed]  
  c.   z0.03 [removed]  
  d.   –z0.25 [removed]  
  e.   –z0.28 [removed]  
  f.   –z0.03 [removed]  

 

Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 14.

 

(b)

Write the equation that gives the z score corresponding to a Stanford–Binet IQ test score.

 

  z  =  (x – [removed] ) / [removed]  

 

(c)

Find the probability that a randomly selected person has an IQ test score. (Round your answers to 4 decimal places.)

 

             
 1.  P(x > 139) [removed]        
 2.  P(x < 75) [removed]        
 3.  P(84 < x < 116) [removed] [removed]   = [removed]  
 4.  P(-2.43 < z < 2.43) [removed]        

 

(d)

Suppose you take the Stanford–Binet IQ Test and receive a score of 122. What percentage of people would receive a score higher than yours? (Round your answer to 2 decimal places.)

 

A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain between 15.98 ounces and 16.02 ounces. A jar is selected from the process every half an hour until a sample of 100 jars is obtained. When the fills of the jars are measured, it is found that formula26.mml = 16.0024 and s = 0.02454. Using formula26.mml and s as point estimates of μ and σ, estimate the probability that a randomly selected jar will have a fill, x, that is out of specification. Assume that the process is in control and that the population of all jar fills is normally distributed. (Round the z-values to 2 decimal places and final answer to 4 decimal places. Negative amounts should be indicated by a minus sign.)


  Using the cum. normal table z < [removed] ) + z > [removed] ) = [removed]

[removed] %  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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