Question 7
A researcher records the number of bar press a rat performs a week. Assuming these data are normally
distributed, what is the probability that the lab rat will press a bar 100 times a week?
(A)
(B)
©
(D)

To find the probability that a lab rat will press the bar 100 times a week, we first need to standardize the value using the Z-score formula:

Where:

Calculating the Z-score:

Next, we look up the Z-score of 2.51 in a standard normal distribution table, or use a calculator. This gives us the area to the left of this Z-score. The area to the left of is approximately 0.9936.

To find the probability of the rat pressing the bar 100 times or fewer, we subtract this area from 1:

To find the probability exactly for pressing 100 times, since it’s a continuous distribution, we will consider a small interval around 100 (like 99.5 to 100.5) which essentially gives us an infinitesimally small width, typically resulting in a very small number. Thus, while this specific probability is not the options given (which seem to relate to the area around 100), it’s important to check the calculations corresponding to the given options in context.

The closest value would be (D) as it corresponds to cumulative probability behavior around the mean in a normal distribution setup.

So, the answer is:
(D)