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Need help with this normal distribution problem

 
 
Reply Wed 18 Mar, 2020 02:28 pm
A professor for a social class is stating that, historically, the distribution for diploma grades in the course resemble a normal distribution with a mean diploma mark of μ=61% and a standard deviation of σ=9%.
What is the probability that a random chosen diploma mark in this course will be at least 74%?
 
engineer
 
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Reply Wed 18 Mar, 2020 02:53 pm
@james wilson,
74 is 13 greater than the mean of 61. This means you are looking for a score at least 13/9 standard deviations greater than the mean. This is your Z score (1.44). If you look up that z score you will find that 92.5% of scores are lower than that, so 7.5% are that value or higher.
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