Final answer:
X represents the number of times a reader's eye fixated on a single word before moving past that word in a cognitive science experiment. The probability of specific values of X can be found using the Poisson distribution. The distribution for X is not exponential.
Step-by-step explanation:
a. In this experiment, X represents the number of times a reader's eye fixated on a single word before moving past that word.
b. X~ means that X follows a Poisson distribution, which is a probability distribution that describes the number of events occurring in a fixed interval of time or space, given an average rate of occurrence.
c. In this experiment, X represents the number of times a reader's eye fixated on a single word before moving past that word.
d. P(X=s) is the probability that X takes on a specific value, in this case, s. For example, P(X=3) would be the probability that the reader's eye fixated on a single word exactly three times before moving past that word.
e. Before doing any calculations, the probability that an individual attention span is less than 10 minutes is likely to be higher than the probability that the average attention span for the 60 children is less than 10 minutes. This is because the average of a larger sample tends to be more stable and closer to the population mean.
f. To calculate the probabilities, we can use the formula for the Poisson distribution: P(X=x) = (e^-λ * λ^x) / x!, where λ is the mean number of events and x is the specific value we are interested in. Plug in the values and calculate the probabilities for parts (e).
g. The distribution for X is not exponential because the exponential distribution describes the time between events in a Poisson process, whereas the Poisson distribution describes the number of events in a given time or space interval.