SOLUTION: You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and t

Question 1082021: You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. The middle 86.64% of the students will score between which two scores?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
From the table, the 0.9332 probability is at z=1.50
therefore, the probability of a score >90 is probability of z>1.50.
z=(x-mean)/sd
1.5=15/sd
1.5 sd=15
sd=10
Between 55 and 60 is z=-2 to z=-1.5. From the table, that is 0.0441, as it should be
The middle 86.64% leaves 13.32% on either side or 6.66%
To confirm, on the calculator, this is between z of -1.5 and z of +1.5 or 15 on either side of the mean.
Answer (60, 90)
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