Question

The time taken by a randomly selected student to fill out an online SOTE has a normal distribution with mean 2 minutes and standard deviation 45 seconds. Suppose 4 students fill out an online SOTE on a randomly selected day. Find the probability that the sample average amount of time taken is at most 3 minutes.

Answer 1

Given that,

mean = = 2

standard deviation = = 45 seconds. =0.75 minutes

n = 4

= 2

=  / n = 0.75 / 4=0.375

P( < 3) = P[( - ) / < (3-2) /0.375 ]

= P(z <2.67)

Using z table  

= 0.9962   

probability= 0.9962