Question

The mean time it is taking a group of students to finish a statistics homework is 105 minutes with standard deviation of 19 minutes. Assume that the time is approximately normally distributed.

a) Within which limits you would expect approximately 50% of the students to complete the homework? 95% of the students?

b) In the group the finishing times were 76, 98, 93, 115, 65, 117. Check the data for outliers.

c) If you do not assume normality for time distribution, would your conclusion about outlier(s) change? Explain.

Answer 1

a). In a Normal distribution, we know that . Hence, the limit I expect approximately 50% of the studenst to c0mpltete the tets is 105 minutes.

95% of the students is that value of a for which We can find the value of a from tables as a=1.6449. Therefore the original limit is

  . Therefore the limit is 136.2531 minutes.

b). From Normal theory, we know that it is rare to find values beyong or . The value 65 seems to be lower than =67. Hence, teh value 65 is an outlier.

c). Yes, if Normality assumption is not made, my conclusion about outlier will change. Since for Normal distribution, will includ e95% of the population.