Question

7) The time it takes college freshman to complete the Mason Basic Reasoning Test is normally distributed with a mean of 24.6 minutes with a standard deviation of 5.8 minutes.

a) What is the probability that a college freshman will take more than 35 minutes to complete the exam?

b) What is the probability that a student will take less than 20 minutes to complete the exam?

Answer 1

Solution :

Given ,

mean = = 24.6

standard deviation = = 5.8

P(x >35 ) = 1 - P(x<35 )

= 1 - P[ X - / / (35-24.6) /5.8 ]

= 1 - P(z <1.79 )

Using z table

= 1 - 0.9633

= 0.0367

probability= 0.0367

(B)

P(X<20 ) = P[(X- ) / σ   < (20-24.6) /5.8 ]

= P(z <-0.79 )

Using z table

= 0.2148

probability =0.2148