For a normally distributed set of scores with, what is the probability of a score being between 180 to 220? $$\mu = 200 \text { and } \sigma = 20$$
A).3413
B).5000
C).6826
D).9544

Question

Quizplus · Accepted Answer

Using the z-score formula: 
$$z = \frac{x-\mu}{\sigma}$$
For x = 180: 
$$z = \frac{180-200}{20} = -1$$
For x = 220: 
$$z = \frac{220-200}{20} = 1$$
Using the z-table, we can find the probability that the score is between -1 and 1:
$$P(-1 < z < 1) = P(z<1) - P(z<-1) = 0.8413 - 0.1587 = 0.6826$$
Therefore, the probability of a score being between 180 to 220 is 0.6826 or 68.26%.

For a Normally Distributed Set of Scores With, What Is μ=200 and σ=20\mu = 200 \text { and } \sigma = 20μ=200 and σ=20

For a Normally Distributed Set of Scores With, What Is $\mu = 200 \text { and } \sigma = 20$