Question 698347: Exam Scores. The grades in an exam followed a normal(75,8)distribution.A student who took the exam is taken at random.
(a)What is the probability that student's score is above 90?
(b) What is the probability that the student's score is between 80 and 90?
(c) What is the probability that the student's score is below 60?
Answer by Positive_EV(69)   (Show Source):
You can put this solution on YOUR website! For each section, you'll need to find a z-value or set of z-values, and use a table to find the appropriate probabilities.
 , where X is the value, mu; is the mean, and sigma is the standard deviation.
1)  . If you look up Z = 1.88 (most Z-tables round to the nearest hundreth) on a Z-table such as http://lilt.ilstu.edu/dasacke/eco148/ztable.htm, you will get the value .9699. The value on the Z-table given is the probability that a random Z-value is less than the Z-value on the table. Thus, the probability the student scores less than 90 is .9699, and the probability he scores above 90 is 1 - .9699 = .0301.
2)  . The probability on the Z-table corresponding to Z = .63 is .7357. Again, since this is the probability that the value has a lower Z-score than .63, the probability the student scores above an 80 is 1 - .7357 = .2643. In order to find the probability of scoring between 80-90, you will need to subtract the probability the student scores above a 90 from the probability the student scores above an 80. This value is .2643 - .0301 = .2342.
30  . Reading the value of Z = -1.88 from the table gives the value .0301. Since the table gives the probability of a score lower than the Z-value, and this is the value you are looking for in this case, the probability of scoring less than 60 is read directly from the table and is equal to .0301.
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