Let the variance of a normally distributed random sample be 16.A point that is 8 units away from the mean is 1-a point such that the probability of getting any other point further from the mean is less than 0.025. 2-a point such that the probability of getting any other point further from the mean is less than or equal to .95. 3-a point such that the probability of getting any other point further from the mean is greater than 0.025. 4-two standard deviations away from the mean.
A)1
B)2
C)3
D)4
E)1 and 4

Question

Quizplus · Accepted Answer

The variance is 16, so the standard deviation is 4. A point 8 units away from the mean is 2 standard deviations away (8/4 = 2), which corresponds to approximately 95% of the data within this range in a normal distribution. Thus, the probability of being further is less than 0.025, satisfying statement 1, and it is also two standard deviations away, satisfying statement 4.

Let the Variance of a Normally Distributed Random Sample Be