Question

a normal distribution has a mean of 50 and a standard deviation of 6. What is the probability that a value selected at random from this data is in the interval from 38 to 56? express your answer as a percent rounded to the nearest tenth.
a) 79.5%
b)81.5%
C)85%
d) 90%

Answer 1

@kropot72

Answer 2

The lower limit of the given interval is two standard deviations below the mean and the upper limit is one standard deviation above the mean. The z-scores are therefore -2 and 1 respectively. Do you know how to use a standard normal distribution table?

Answer 3

no i do not @kropot72

Answer 4

Then do you know how you are expected to solve this question? For example some models of statistical calculator have the required functionality.

Answer 5

im honestly not quite sure at all. thats why i need help @kropot72

Answer 6

The table here enables you to find the cumulative probability for z scores of -2.0 and 1.0.
http://www.math.bgu.ac.il/~ngur/Teaching/probability/normal.pdf
Find the z-score in the first column on the left side and read the value in the next column, which is headed 0.00. Can you do that for the z-score of -2.0?

Answer 7

would it be 68% because if falls within one standard deviation? @kropot72

Answer 8

No. As I posted previously:
"The lower limit of the given interval is two standard deviations below the mean and the upper limit is one standard deviation above the mean."

Answer 9

oh.

Answer 10

would it be 81.5%?

Answer 11

@kropot72 ^^

Answer 12

How did you work that out?

Answer 13

is it correct? @kropot72

Answer 14

Was that a guess then, if you can't explain briefly how you arrived at that value?

Answer 15

It appears that you know the '68 - 95 - 99.7' rule for a normal distribution. That rule can be used on this question.