Question
Question 7
A researcher records the number of bar press
distributed, what is the probability that the lab rat will press a bar 100 times a week?
(A)
(B)
©
(D)
A researcher records the number of bar press
distributed, what is the probability that the lab rat will press a bar 100 times a week?
(A)
(B)
©
(D)
Ask by Mccoy Norris. in the United States
Mar 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that the lab rat will press the bar 100 times a week is approximately 0.4940, so the answer is (A).
Solution
To find the probability that the lab rat will press a bar 100 times a week, we can use the properties of the normal distribution.
Given:
- Mean (
) = 78.4 - Standard Deviation (
) = 8.6 - We want to find
.
First, we need to calculate the z-score for
Substituting the known values:
Now, let’s calculate the z-score.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Remove the parentheses:
- step2: Subtract the numbers:
- step3: Convert the expressions:
- step4: Multiply by the reciprocal:
- step5: Reduce the numbers:
- step6: Multiply:
The calculated z-score is approximately.
Next, we will find the probability
Let’s calculate
It seems I cannot directly calculate the cumulative probability for the z-score. However, I can provide the approximate value based on standard normal distribution tables or calculators.
It seems I cannot directly calculate the cumulative probability for the z-score. However, I can provide the approximate value based on standard normal distribution tables or calculators.
For a z-score of approximately
To find the probability of the rat pressing the bar 100 times or more, we need to calculate:
Thus, we can compute:
However, since we are looking for the probability of pressing the bar less than or equal to 100, we can use the cumulative probability directly.
Given the options provided:
(A)
(B)
©
(D)
(A)
(B)
©
(D)
The closest value to
Thus, the answer is:
(A)
(A)
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Explain 
Simplify this solution The Deep Dive
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:
-
(the value we are interested in) -
(mean) -
(standard deviation)
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
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)
So, the answer is:
(D)
(D)
