A set of data is normally distributed with a mean of 500 and standard deviation of 40.
a). What percent of the data is between 460 and 540?
P(460<x<540)=P(-1<z<1)
=0.8413-0.1587
=0.6826
b). Find the probabilty that a value selected at random is less than 420.
P(x<420)=P(z<(420-500)/40)
=P(z<-2)
=0.0228
are these right?
both correct.
You might find this applet very useful.
http://davidmlane.com/hyperstat/z_table.html
It eliminates the use of charts and tables, you you don't even have to convert to z-scores
Yes, your calculations are correct. To find the probability between 460 and 540, you need to standardize the values using z-scores. You correctly calculated the z-scores for 460 and 540 as -1 and 1 respectively. Then, you used the standard normal distribution table to find the corresponding probabilities: P(z < 1) = 0.8413 and P(z < -1) = 0.1587. Subtracting the second probability from the first gives you the probability of the data falling between 460 and 540, which is 0.6826.
Similarly, to find the probability that a value selected at random is less than 420, you need to calculate the z-score for 420 using the formula (420 - 500) / 40 = -2. Then, you looked up the probability corresponding to a z-score of -2 in the standard normal distribution table, which is approximately 0.0228.
So, overall, your calculations are correct.