a set of 50 data values has a mean of 18 & variance of 4 find the probability of a data value <20 find the standard score z for data value = 20please explain and show work

1 Answer | Add Yours

embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

We are given a set with n=50, `bar(x)=18` , and `sigma=4` .

Find the probability that a data value is less than 20:

Convert 20 to a `z` score:


Then `P(x<20)=P(z<0.50)=.6915` or 69.15% will be less than 20


Since you were given n, I wonder if your actual question is about a sample mean, not an actual data value. If that is the case, the question is what is the probability of obtaining a sample mean less than 20 if the sample size is 50:

Convert 20 to a z-score; note that since this is from a sample we use `z=(x-mu)/(sigma/sqrt(n))` :


Then `P(x<20)=P(z<3.54)` From a standard normal table we find `P(z<.54)=.9998` (Most tables stop at z=3.5 -- this value is from a graphing calculator.)

We’ve answered 317,595 questions. We can answer yours, too.

Ask a question