Determine a normal standard deviation and calculate a lower-tail probability.
Determine a normal standard deviation and calculate a lower-tail probability.
7 marks
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The scores of a test given to students are normally distributed with a mean of 21. 80 % of the students have scores less than 23.7.
Find the standard deviation of the scores. A student is chosen at random. This student has the same probability of having a score less than 25.4 as having a score greater than b.[3]
[4]
Find the probability the student has a score less than 25.4.
Find the value of b.
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Answer:\(P(X<25.4)=0.915\). Equal tail areas about the mean imply \(b=2(21)-25.4=16.6\).