Question

The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. (z (X-μ)/σ)

μ=

σ=

A) If students are given 85 minutes to complete the exam, what probability that students will not finish?

B) What percent of students will complete the exam between 63 minutes and 80 minutes?

Answer 1

Part a)

P ( X > 85 ) = 1 - P ( X < 85 )
Standardizing the value

Z = ( 85 - 70 ) / 10
Z = 1.5

P ( Z > 1.5 )
P ( X > 85 ) = 1 - P ( Z < 1.5 )
P ( X > 85 ) = 1 - 0.9332
P ( X > 85 ) = 0.0668

Part b)

P ( 63 < X < 80 )
Standardizing the value

Z = ( 63 - 70 ) / 10
Z = -0.7
Z = ( 80 - 70 ) / 10
Z = 1
P ( -0.7 < Z < 1 )
P ( 63 < X < 80 ) = P ( Z < 1 ) - P ( Z < -0.7 )
P ( 63 < X < 80 ) = 0.8413 - 0.242
P ( 63 < X < 80 ) = 0.5994

To find percentage = 0.5994 * 100 = 59.94%