Using the Central Limit Theorem. In Exercises 5–8, assume that SAT scores are normally distributed with mean
??
= 1518 and standard deviation
??
= 325 (based on data from the College Board).
1)
a.
If 1 SAT score is randomly selected, find the probability that it is less than 1500.
b.
If 100 SAT scores are randomly selected, find the probability that they have a mean less than 1500.
2)
a.
If 1 SAT score is randomly selected, find the probability that it is greater than 1600.
b.
If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600.
3)
a.
If 1 SAT score is randomly selected, find the probability that it is between 1550 and 1575.
b.
If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575.
c.
Why can the central limit theorem be used in part (b), even though the sample size does not exceed 30?
4)
a.
If 1 SAT score is randomly selected, find the probability that it is between 1440 and 1480.
b.
If 16 SAT scores are randomly selected, find the probability that they have a mean between 1440 and 1480.
c.
Why can the central limit theorem be used in part (b), even though the sample size does not exceed 30?