4.19 4-72 Probability Distributions 1A primary contractor for the Delta Rocket p

Question

4.19

4-72 Probability Distributions 1A primary contractor for the Delta Rocket purchases bolts from a maching shop. The contractor requires the bolts to have a diameter between 2.6 and 2.7 cm. The machine shop produces bolts whose diameters are normally distributed with a mean diameter of 2.65 cm and a standard deviation of 02 em.. Find the proportion of bolts outside the specifications. 20 The Dual Probe Precision Digital Thermometer is used to measure the emperaure of any liquid solution. The difference between the tue emperature and the measured temperature is a normally distributed random variable with a mean of0 Centigrade(C) and a standard deviation of 0.5 C. Find the probability tiat a measured temperature is inaccurate by more than 1°C.

Explanation / Answer

4.19

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    2.6      
x2 = upper bound =    2.7      
u = mean =    2.65      
          
s = standard deviation =    0.02      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -2.5      
z2 = upper z score = (x2 - u) / s =    2.5      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.006209665      
P(z < z2) =    0.993790335      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.987580669      

Thus, those outside this interval is the complement =    0.012419331   [ANSWER]  

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