Answer:
Step-by-step explanation:The question asks about the range of x values within which 95% of the data lies for a normally distributed random variable X with a mean of -3 and a standard deviation of 1.
To find the range of x values, we can use the properties of the normal distribution and the concept of standard deviations.
In a standard normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Since we are given that the mean of X is -3 and the standard deviation is 1, we can use these percentages to find the range of x values within which 95% of the data lies.
First, we determine the number of standard deviations that correspond to 95% of the data. We know that 95% corresponds to two standard deviations in a standard normal distribution.
Next, we convert the standard deviations to actual x values by multiplying the standard deviation by the appropriate number of standard deviations and adding or subtracting it from the mean.
For the lower x value, we subtract two standard deviations from the mean:
-3 - (2 * 1) = -5.
For the upper x value, we add two standard deviations to the mean:
-3 + (2 * 1) = -1.
Therefore, 95% of the data lies between the x values -5 and -1.