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Question 318:



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First thing you should notice that both values are less than the mean, so we should expect negative z-scores and areas less than 50%.  You'll need to find two areas under the normal curve given the mean of 61.3 and standard deviation 3.3.

  1. Find the normal deviate or z-score for the larger value : (60-61.3)/3.3 = a z-score of -.3939.  
  2. Find the area under the normal curve using the z-score to percentile calculator, choose 1-sided area. This provides an area of about 34.68%. 
  3. Subtract the smaller area, which following the same steps above is (55-61.3)/3.3= -1.909  and has area of ~2.82%. Subtracting the smaller gets us 34.68-2.82 = 31.9%

So the probability a car is going between 55 and 60 miles an hour is about 31.9%. You can also visualize this area by taking a look at the interactive graph of the standard normal curve and enter in the IQ mean of 61.3 and SD of 3.3.

See also question 289

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