Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to four decimal places.
A)0.9867
B) 0.8026
C) 0.8016
D) 0.4013
E) 0.8036

Question

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to four decimal places.  
A)0.9867
B)  0.8026
C)  0.8016
D)  0.4013
E)  0.8036

Quizplus · Accepted Answer

The probability that a normal variable is more than $\frac { 1 } { 4 }$ standard deviations away from its mean is found by looking at both tails beyond $\frac { 1 } { 4 }$ standard deviations from the mean. The Z-score for $\frac { 1 } { 4 }$ standard deviations is 0.25. Looking up the Z-score of 0.25 in a standard normal distribution table or using a calculator, we find that the area to the right of Z = 0.25 is approximately 0.4013. Since we are interested in both tails (more than $\frac { 1 } { 4 }$ standard deviations away means both above and below the mean), we double this value to get approximately 0.8026.

Find the Probability That a Normal Variable Takes Values More 14\frac { 1 } { 4 }41​

Find the Probability That a Normal Variable Takes Values More $\frac { 1 } { 4 }$