Question

SAT scores have a mean of 1000 and a standard deviation of 220.

Q18: What is the probability that a random student will score more than 1400?

Q19: Using the Central Limit Theorem, what is the probability that sample of 100 students will have an average score less than 990?

Q20: Using the Central Limit Theorem, what is the probability that sample of 100 students will have an average score between 990 and 1010?

Use excel functions to calculate your answers.

Answer 1

Question 18

P ( X > 1400 ) = 1 - P ( X < 1400 )
Standardizing the value

Z = ( 1400 - 1000 ) / 220
Z = 1.82

P ( Z > 1.82 )
P ( X > 1400 ) = 1 - P ( Z < 1.82 )
P ( X > 1400 ) = 1 - 0.9656
P ( X > 1400 ) = 0.0344

Question 19

P ( X < 990 )
Standardizing the value


Z = -0.45

P ( X < 990 ) = P ( Z < -0.45 )
P ( X < 990 ) = 0.3247

Question 20

P ( 990 < X < 1010 )
Standardizing the value


Z = -0.45

Z = 0.45
P ( -0.45 < Z < 0.45 )
P ( 990 < X < 1010 ) = P ( Z < 0.45 ) - P ( Z < -0.45 )
P ( 990 < X < 1010 ) = 0.6753 - 0.3247
P ( 990 < X < 1010 ) = 0.3506