In: Statistics and Probability
The distance a student lives (in miles) from their classroom is approximately normally distributed with a mean of 5 miles and a standard deviation of 1.5 miles. Use the normal table to find the probabilities.
a) How far away do the closest 15% of students live?
b) What is the probability that a student will live less than 7 miles away?
c) What is the probability that a student will live further away than 3 miles
or less than 7 miles away?
Answer a)
Let x miles be the value below which 15% of of students live
P(X < x) = 0.15
Let z be the z score corresponding to x.
Therefore, P(Z < z) = 0.15
z value based on standard normal table is -1.04
z = (x-μ)/σ
-1.04 = (x-5)/1.5
x = 5 - 1.04*1.5
x = 3.44
The closest 15% of students live 3.44 miles away
Answer b)
The probability that a student will live less than 7 miles away is 0.9082
Answer c)
P ( −1.33<Z<1.33 ) = P(Z<1.33) - P ( Z<-1.33) = 0.9082-0.0918
P ( −1.33<Z<1.33 ) = 0.8164
The probability that a student will live further away than 3 miles or less than 7 miles away is 0.8164