Question
The scores on a national achievement test are normally distributed with a mean of 50 and a standard deviation of 10. Out of a group of 200 students, how many would you expect to score more than 70?
Answers
MathMate
μ=50, σ=10;
For score 70, convert to standardized value
z=(x-μ)/σ=(70-50)/10=2
P(x>70)=P(z>2)
Look up standard normal distribution table to get
P(z<=2)=0.9772, so
P(x>70)=P(z>2)=1-0.9772=0.0228
or the average number of students with score of 70 or more
= P(x>70)*200=4.56 = 5 approx.
For score 70, convert to standardized value
z=(x-μ)/σ=(70-50)/10=2
P(x>70)=P(z>2)
Look up standard normal distribution table to get
P(z<=2)=0.9772, so
P(x>70)=P(z>2)=1-0.9772=0.0228
or the average number of students with score of 70 or more
= P(x>70)*200=4.56 = 5 approx.