Complete Question
From the mid-1960's to the early 1990's, there was a slow but steady decline in SAT scores. For example, take the Verbal SAT. The average in 1967 was about 543; by 1994, the average was down to about 499. However, the SD stayed close to 110. The drop in average has a large effect on the tails of the distribution.
Estimate the percentage of students scoring over 700 on 1967.
A 0.7%
B 7%
C 7.67%
D 7.6%
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The average SAT score in 1967 is [tex]\= x_1 =543[/tex]
The standard deviation of score in 1967 is [tex]\sigma_ 1= 110[/tex]
The average SAT score in 1994 is [tex]\= x_2 = 499[/tex]
The standard deviation of score in 1967 is [tex]\sigma_ 2 = 110[/tex]
The percentage of students scoring over 700 on 1967 is mathematically represented as
[tex]P(X > 700)[/tex]
Where X is the random variable representing score of student above 700
Now normalizing the above probability we have
[tex]P(X > 700) = P(Z > \frac{700 - \= x_1 }{\sigma } )[/tex]
substituting values
[tex]= P(Z > \frac{700 - \= 543}{110 } )[/tex]
[tex]= P(Z > 1.83 )[/tex]
Form the normalized z table
= 0.076
= 7.6 %
