Question

A biologist wants to see if rats running in a maze use some kind of decision process on how to proceed when they come to an intersection. To do so she decides to simulate the situation by assuming the decisions are random, so she creates a “virtual rat” that at each intersection tosses a coin to decide which way to go. She lets the “virtual rat” run the maze 1000 times, and finds the average length run is 14.8 feet, with a standard deviation of 2.4 feet. She then lets a real rat run the maze, and measures the length run to be 13 feet. Explain what conclusion the biologist can make.

Answer 1

We can find the probability of running length 13 feet by using normal distribution

We first need to find the z-score which is given by applying the following formula:

z-score = (X-μ) ÷ σ

Where:
μ is the average
σ is the standard deviation
X is the sampled value

z-score = (13-14.8) ÷ 2.4
z-score = -0.75

finding the probability, or the p-value by looking up on the z-table

P(Z<z) = P(Z<-0.75) = 0.2266

The conclusion that the biologist could make is that out of 1000 virtual rat, there are 0.2266×1000 = 226.6 ≈ 227 virtual rats that run the maze with length of 13 feet