# Pt1420 Unit 6 Case Study

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Application:

1. Find the area under the standard normal curve between z = 0 and z = 1.65.

Answer: The value 1.65 may be written as 1.6 to .05, and by locating 1.6 under the column labeled z in the standard normal distribution table (Appendix 2) and then moving to the right of 1.6 until you come under the .05 column, you find the area .450 . This area is expressed as

2. Find the area under the standard normal curve between z = -1.65 and z = 0.

Answer: The area may be represented as . Since the normal curve is symmetric, then

3. Find the area under the standard normal curve between z = -1.65 and z = 1.96.

Answer: The area may be represented as. This may be broken down
Scores on the SAT Verbal Test in recent years follow approximately normal distribution with mean 505 and standard deviation 110. How high must the student score in order to place in the top 100% of all students taking the SAT?

Answer: Being in the top 100% implies having at least the 90th percentile. The entry in the standard normal distribution table that is closest to .9 is 0.3997 + 0.5. The value of z that corresponds to this is 1.28. Hence,

Exercises:

1. An important measure of the performance of a locomotive is its adhesion, which is the locomotives pulling force as a multiple of its weight. The adhesion of a 440 horsepower diesel locomotive varies in actual use according to a normal distribution with mean = 0.37 and standard deviation = 0.04, a.) What proportion of adhesions measures higher than 0.40? b.) What proportion of adhesions is between 0.40 and 0.50?