SAT scores are found to be normally distributed with a mean of 21 and a standard
ID: 2936729 • Letter: S
Question
SAT scores are found to be normally distributed with a mean of 21 and a standard deviation of 4.5. Answer the following: (a) Determine the z-score for a person from this population that has an SAT score of 23. Then find the z-score for someone whose SAT score is 15 (b) If x represents a possible SAT score from this population, find P(x > 23). (c) Find P(20 < x < 25) and write a sentence for the interpretation of this value. (d) The top 10% of all people in this group have SAT scores high enough to earn a scholarship. Determine the SAT score which is high enough to earn the scholarship. SAT scores are found to be normally distributed with a mean of 21 and a standard deviation of 4.5. Answer the following: (a) Determine the z-score for a person from this population that has an SAT score of 23. Then find the z-score for someone whose SAT score is 15 (b) If x represents a possible SAT score from this population, find P(x > 23). (c) Find P(20 < x < 25) and write a sentence for the interpretation of this value. (d) The top 10% of all people in this group have SAT scores high enough to earn a scholarship. Determine the SAT score which is high enough to earn the scholarship.Explanation / Answer
as z score =(X-mean)/std deviaiton
a) hence z score for SAT score of 23 =(23-21)/4.5=0.4444
z score for SAT score is 15 =(15-21)/4.5 =-1.3333
b) P(x > 23) =1-P(X<23)=1-P(Z<0.4444)=1-0.6716 =0.3284
c)
P(20 < x < 25) =P((20-21)/4.5<Z<(25-21)/4.5)=P(-0.2222<Z<0.8889)=0.8130-0.4121 =0.4009
from above we get that probability of having a score between 20 to 25 is 0.4009.
d)for top 10% ; at 90th percentile z score =1.2816
therefore corresponding value =mean +z*Std deviation =21+1.2816*4.5 =26.77
please revert for any clarification required,
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