Question

Reaction time studies are studies in which participants receive a stimulus and the amount of time it takes for them to react is measured. In one simple type of reaction time study, each participant holds a clicker button and stares at a screen. When the participant sees a part of the screen light up, he or she clicks the button as quickly as possible. The researcher then records how much time elapsed between when the screen lit up and when the participant clicked the button. Suppose that, in these tests, the distribution of reaction times is skewed slightly to the right. Suppose also that mean reaction time is 190 milliseconds, and the standard deviation for reaction times is 20 milliseconds (for the purposes of this problem, you can treat the mean and standard deviation as population parameters). Use this information to answer the following questions, and round your answers to four decimal places.

a. Suppose we have 10 different people take this reaction time test. What is the probability that the average of these 10 reaction times will be greater than 180 milliseconds?

b. Suppose we have 16 different people take this reaction time test. What is the probability that the average of these 16 reaction times will be less than 193 milliseconds?

c. Suppose we have 24 different people take this reaction time test. What is the probability that the average of these 24 reaction times will be less than 183 milliseconds?

Answer 1

µ = 190

sd = 20

a) n = 10

                           

                            = P(Z > -1.58)

                            = 1 - P(Z < -1.58)

                            = 1 - 0.0571

                            = 0.9429

b) n = 16

                           

                           = P(Z < 0.6)

                           = 0.7257

c) n = 24

                           

                            = P(Z < -1.71)

                            = 0.0436