Question

The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below

shows the distribution of times, in seconds, for the 100 mice.
Which of the following values is closest to the standard deviation of the 100 times?
(A) 2.5 seconds
(B) 10 seconds
(C) 20 seconds
(D) 50 seconds
(E) 90 seconds

Answer 1

To estimate the standard deviation of the 100 times recorded, we can examine the histogram provided. Based on the distribution shown, the standard deviation is likely closest to 20 seconds.

Step-by-step explanation:

To find the standard deviation of the 100 times recorded, we can use the formula:

standard deviation = sqrt((sum of (x - mean)^2) / n)

where x represents the individual times, mean is the average time, and n is the number of times.

Since we do not have access to the actual data, we cannot calculate the standard deviation directly. However, based on the histogram provided, we can make an estimation.

Looking at the histogram, we can see that the majority of the times fall within the range of 10 to 30 seconds. Therefore, we can estimate that the standard deviation is closer to the range of (C) 20 seconds.

Answer 2

To find the standard deviation of the 100 times, you need to use the formula for standard deviation. First, find the mean by summing up all the times and dividing by 100. Then, subtract the mean from each individual time and square the result. Finally, sum up all the squared differences, divide the sum by 100, and take the square root of the result to find the standard deviation.

Step-by-step explanation:

To find the standard deviation of the 100 times, we need to use the formula for standard deviation:

σ = √[(Σ(x - μ)²/N)]

where σ is the standard deviation, x is each individual value, μ is the mean, and N is the number of values.

Given that we have the distribution of times for the 100 mice, we can find the mean and standard deviation:

1. Find the mean by summing up all the times and dividing by 100.
2. Subtract the mean from each individual time and square the result.
3. Sum up all the squared differences.
4. Divide the sum by 100.
5. Take the square root of the result to find the standard deviation.

By applying these steps, we can find the closest value to the standard deviation of the 100 times.