Intro to Stats and Analytics

Question

For a standard normal distribution, find:

P(-2.7 < z < 0.17)

Round your probabilty accurate to 4 decimal places.

Answer 1

Hi Lucy,

Standard normal means the distribution has a mean (mu) of 0 and standard deviation (sigma) of 1. The classic equation in introductory statistics:

z = x - mu / sigma

For your problem:

z1 = (-2.7 - 0)/1

That works out to z = -2.7, and your second value works out to z2 = 0.17. That's the main property of the standard normal distribution. Now, go to the z-table and look up the probabilities for both of those values:

P(Z< -2.7) = 0.0035

P(Z< 0.17) = 0.5675

Now, you were given a range, i.e. a < x < b. This means you must subtract the lower probability from the higher. So:

P = 0.5675 - 0.0035

P = 0.5640

I hope this helps.