SOLUTION: Hi, I am having a lot of trouble with Normal Distribution. I do online school and the lessons don't do a very good job of explaining exactly how to solve these problems. My teacher

Question 1081808: Hi, I am having a lot of trouble with Normal Distribution. I do online school and the lessons don't do a very good job of explaining exactly how to solve these problems. My teacher said that all of the following problems were answered incorrectly. Any help is greatly appreciated!!
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Consider this scenario for questions 5 - 8.
A standardized test was given to a set of high school juniors and the distribution of the data is bell shaped. The mean score is 800 and the standard deviation is 120.
5. Between which two scores did 95% of the students score?
6. To qualify for a special summer camp for accelerated students, a student must score within the top 16% of all scores on the test. What score must a student make to qualify for summer camp?
z = +1.96
x = μ+σ*z
x = 74+8(1.96)
x = 89.68
90
7. What score is 1/2 standard deviation above the mean?
z = 1/2
score = 800 + (1/2)120 = 860
8. A student scores 900 on the test. How many more points did the student need to qualify for summer camp?
5/
(800 - 240 , 800+240)
6/
920
7/
800-240
560
Consider the following scenario for questions 9-12.
On the average, members at a local fitness center work out for 90 minutes with a standard deviation of 15 minutes. The distribution is normal.
9. What percentage of the fitness club members work out for 45 minutes or less?
z(45) = (45-90)/15 = -45/15 = -3
P(x <= 45) = P(z <= -3) = (-100,-3)
0.3%

10. What percentage of the fitness club members work out for 2 hours and 15 minutes or more?
z = (135 - 90)/15
3%
11. 68% of the fitness club members work out between which two time intervals?
P(Z < z) = 0.84
0.5+0.34
68% within 1 sd
between 75 and 105 minutes
12. We can say that 99.7% of the fitness club members work out for no more than 135 minutes.
(Mean - 3 � std) and (Mean + 3 � std)
(90 - 3 � 15) and (90 + 3 � 15)
45 � 135

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
mean 800 sd 120
the middle 95% is from z.025 to z.975 which is +/- 1.96
z=(x-mean)/sd
1.96=(x-800)/120
235.2=x-800
x=1035.2 at top end and 664.8 at bottom end
===============
84th percentile from table is z=+0.95
0.95=(x-mean)/120
114=x-800
914= the critical value
==================
Half sd above the mean has a score of 860; 900 is 14 points shy of qualifying.
====================
9 is mostly correct, except 0.3% is double what it should be. The result is 0.0013 or .13%
====================
10 is the same at the opposite end, the per cent more than+3 sd, which is not the same as the per cent more than +/- 3 sd.
===================
11 is correct.
12. We can say that 99.87% work out for no more than 135 minutes.
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