Question

The time required for a student to complete a Statistics exam is normally distributed with a mean of 55 minutes and a standard deviation of 12 minutes.

1. What percent of students take between 40 and 50 minutes to complete an exam?

2. At what point in time will 25 percent of the students have completed the exam?

Answer 1

Solution :

Given that ,

mean = = 55

standard deviation = =12

P(40< x < 50) = P[(40 - 55) /12 < (x - ) / < (50-55) /12 )]

= P( -1.25< Z < -0.42)

= P(Z <-0.42 ) - P(Z <-1.25 )

Using z table   

= 0.3372 - 0.1056

= 0.2316

=23.16%

b.

Using standard normal table,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z <-0.67 ) = 0.25

z = -0.67 Using standard normal z table,

Using z-score formula  

x= z * +

x= -0.67*12+55

x= 46.96

x=47 rounded