Question about probability

Question

A normal distribution has a mean of 30 and a SD of 12. For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion in the body (hint: find z scores).

a. 33

b. 18

c. 24

d. 39

Answer 1

z = (x-μ)/σ

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

for a)

z=(33-30)/12

z = .25

it's difficult for me to understand your question as it is currently written, but a positive z-score/an x value above the mean says this is in the right half of the distribution.

to convert this Z value into a percentile or a proportion, you will use a z table or a function on your statistics software.

P(x<Z) = 0.59871

this means that 60% of the dataset is 33 or less

you can also solve this type of problem using a normal CDF function and not have to do any work by hand the function inputs would be normcdf (0, 33, 30, 12) = .6