distribution

Question

a normal distribution has a mean of 100 with standard deviation of 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between x=90 and x=110

Answer 1

z = (90 - 100)/20 = -10/20 = -0.5

 

z = (110 - 100)/20 = 10/20 = 0.5

 

I use the normal distribution from the Reference Page to figure out the number of standard deviations from the mean based on Common Core standards. 

 

0.5 of a standard deviation = about 38.2%.

1 standard deviation = about 68.2%. 

1.5 standard deviations = about 86.6%.

2 standard deviations = about 95.4%. 

2.5 standard deviations = about 98.8%.

3 standard deviations = about 99.8%.

 

P(90 < X < 110) = P(X < 110) - P(X < 90) = 0.691 - 0.309 = 0.382

 

The probability of the score that will be a value between 90 and 110 is 38.2%.