Question

The time it takes to grade a randomly selected student’s paper varies with a mean of 5.25
minutes and a standard deviation of 4.25 minutes.
a) Is the distribution of grading times Normal? Explain.
b) If the task is to grade 80 randomly selected papers: What is the (approximate) probability
the (sample) mean time to grade these papers exceeds 6 minutes?

Answer 1

solution

(A)it is normal distribution

normal distribution use in any sample size

(B)mean = = 5.25

standard deviation = = 4.25

n = 80

= 5.25

= / n = 4.25/ 80 = 0.4752

P( >6 ) = 1 - P( <6 )

= 1 - P[( - ) / < (6-5.25) /0.4752 ]

= 1 - P(z <1.58 )

Using z table

= 1 - 0.9429

= 0.0571

probability= 0.0571