Which of the following normal distributions has the smallest spread?

A. A normal distribution with mean 1 and standard deviation 3
B. A normal distribution with mean 0 and standard deviation 2
C. A normal distribution with mean 3 and standard deviation 2
D. A normal distribution with mean 2 and standard deviation 1
E. None of the above

To determine which normal distribution has the smallest spread, we need to look at the standard deviation. The smaller the standard deviation, the smaller the spread of the distribution.

Comparing the standard deviations of the given normal distributions:

A. A normal distribution with mean 1 and standard deviation 3
B. A normal distribution with mean 0 and standard deviation 2
C. A normal distribution with mean 3 and standard deviation 2
D. A normal distribution with mean 2 and standard deviation 1

Out of these options, the normal distribution with the smallest spread is option D. A normal distribution with mean 2 and standard deviation 1.

Therefore, the answer is D.

To determine which normal distribution has the smallest spread, we need to compare the standard deviations. The standard deviation is a measure of how spread out the data points are in relation to the mean.

A normal distribution with a smaller standard deviation means that the data points are closer to the mean and therefore less spread out.

Let's compare the standard deviations of each normal distribution:

A. A normal distribution with mean 1 and standard deviation 3
Standard deviation = 3

B. A normal distribution with mean 0 and standard deviation 2
Standard deviation = 2

C. A normal distribution with mean 3 and standard deviation 2
Standard deviation = 2

D. A normal distribution with mean 2 and standard deviation 1
Standard deviation = 1

From the above comparisons, we can see that option D, a normal distribution with mean 2 and standard deviation 1, has the smallest spread. The standard deviation is the lowest among all the given options.

Therefore, the answer is D. A normal distribution with mean 2 and standard deviation 1.

Standard deviation is a measure of spread. Choose the smallest spread among responses A to D.