Standard Normal Distribution and Probability Calculations

This paper covers the concept of standard normal distribution and its application in probability calculations.

Ethan Wilson

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Standard Normal Distribution and Probability CalculationsQuestion 1. 1. Find the standardized variable z if x has Mean 12 and standard deviation 4. (Points :1)Z = (x-4)/12Z = (12-x)/4z = (x-12)/4Z = (x+12)/4Question 2. 2. Find the areaunder the standard normal curve to the right of z = 1.55. Round to fourdecimal places. (Points : 1).9394.9505.0606.0485Question 3. 3. Find the area under the standard normal curve to the left of z = 2.63 (Points : 1).0043.0102.9957.9959Question 4. 4. Find the area under the standard normal curve over the interval z = −0.44 to z = 0.44.Compute probabilities using the standard normal table in Appendix B (Table 3). Round the answer tofour decimal places. (Points : 1)0.33000.34000.35000.3600Question 5. 5. Scores on a certain nationwide college entrance examination follow a normaldistribution with a mean of 550 and a standard deviation of 100. Find the probability that a student willscore over 680. Round your answer to four decimal places. (Points : 1)0.1587

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