Answer to Question #265695 in Statistics and Probability for muzondiwa

Question

using the standard normal tables,find the given probabilities

1)P(Z<or=1)

2)Z(Z>or=0.5)

3)Z(-0.8<Z<1.5)

Answer 1

Z means stantard normal distribution, then Z is a continious random variable, which means $\forall x\in X:P(Z=x)=0$

There are a lot of such tables in the Internet, i will attach one of them

That table shows P(0 < Z < x), so, P(Z < x) will be 0.5 + P(0< Z < x)

1) P(Z ≤ 1) = P(Z < 1) = 0.5 + 0.3413 = 0.8413

2) P(Z ≥ 0.5) = 1 - P(Z < 0.5) = 1 - 0.5 - 0.1915 = 1 - 0.6915 = 0.3085

3) P(-0.8 < Z < 1.5) = P(Z < 1.5) - P(Z < -0.8) = (0.5 + 0.4332) - (0.5 - 0.2881) = 0.7213