SOLUTION: Scores for a particular standardized test are normally distributed with a mean of 80 and a standard deviation of 14. Find the probability that a randomly chosen score is i. No gr

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Question 1183992: Scores for a particular standardized test are normally distributed with a mean of 80 and a
standard deviation of 14. Find the probability that a randomly chosen score is
i. No greater than 70
ii. At least 95
iii. Between 70 and 95
iv. A student was told that her percentile score on this exam is 72%. Approximately
what is her raw score?
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd
a. z < (70-80)/14 or -5/7. That probability is 0.2375
b. z> (95-80)/14 or 15/14. That probability is 0.1420
c. The probability for this is 1- the sum of the above two, since this is all that is left. It is 0.6205
Check with 2nd VARS 2 normalcdf (70,95,80,14) ENTER
d. 72nd percentile is where probability=0.7200 VARS 3invnorm (0.72,0,1) yields a z=0.5828
so (x-80)=0.5828*14=8.16
and the score would be 88.16 as a raw score or 88.

Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website!
i. No greater than 70

On your TI-84, press 2ND press VARS press 2 Make the screen read: normalcdf lower:-9999999 upper:70 μ:80 σ:14 Paste Scroll down with the down arrow to Paste Press ENTER Read on the screen normalcdf(-9999999,70,80,14) Press ENTER Read 0.2375251875 round to 0.2375 --------------------------------------------

ii. At least 95
Same as above except lower:95 upper:99999999 Read 0.1419884174 round to 0.1420 --------------------------------------------

iii. Between 70 and 95
Same as above except lower:70 upper:95 --------------------------------------------

iv. A student was told that her percentile score on this exam is 72%. Approximately
what is her raw score?
On your TI-84, press 2ND press VARS press 3 Make the screen read: invnorm area:0.72 μ:80 σ:14 Paste Scroll down with the down arrow to Paste Press ENTER Read on the screen invNorm(0.72,80,14) Press ENTER Read 88.15978103 Round to 88.16 or as your teacher tells you. Edwin