The time required to assemble an electronic component is normally distributed wi

Question

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 24 minutes and 16 minutes, respectively. Use Table 1.

Find the probability that a randomly picked assembly takes between 19 and 29 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

It is unusual for the assembly time to be above 45 minutes or below 7 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Find the probability that a randomly picked assembly takes between 19 and 29 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Explanation / Answer

A)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    19      
x2 = upper bound =    29      
u = mean =    24      
          
s = standard deviation =    16      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.31      
z2 = upper z score = (x2 - u) / s =    0.31      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.378280478      
P(z < z2) =    0.621719522      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.243439044   [ANSWER]

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B)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    7      
x2 = upper bound =    45      
u = mean =    24      
          
s = standard deviation =    16      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.06      
z2 = upper z score = (x2 - u) / s =    1.31      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.1445723      
P(z < z2) =    0.904902082      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.760329783      

Thus, those outside this interval is the complement = 0.239670217   [ANSWER]
  

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