Question

PLEASE HELPPPPPPPPPPP A set of 750 data points are normally distributed with a mean of 500 and a standard deviation of 35.



a) What is the probability that a value will be between 430 and 500?

b) What is the probability that a value will be above 535?

c)How many data points have values between 465 and 500?

Answer 1

Do you understand the normal distribution curve in your attachment?

Answer 2

Not really

Answer 3

The mean is shown by the central ordinate labelled 0 on the horizontal axis.
The position of points spaced various numbers of standard deviations from the mean is represented by the ordinates labelled 1, -1; 2, -2 and 3, -3 on the horizontal axis.

If you look at the central ordinate ( labelled 0) and the first ordinate to the left of it (labelled -1) you will see that 34% of the data points under the curve lie between the mean and -1 standard deviation from the mean.
If you look at the ordinates labelled -1 and -2 you will see that 13.5% of the data points lie between -1 and -2 standard deviations from the mean.

Therefore the number of data points between the mean and -2 standard deviations from the mean = 34 + 13.5 = 47.5% of the total data points.

Do you follow so far?

Answer 4

Yes i do follow !! Thanks for breaking it down

Answer 5

Good!
Looking at part a) of your question, 430 lies 2 standard deviations below the mean. Therefore the probability that a value will be between 430 and 500 is 47.5% or 0.475.