Question

Find

a. P(Z=1.32)

b. P(Z>5)

c. P(-1<Z<1)

d. P(-2<Z<2)

e. P(-3<Z<3)

(c, d, and e form what is called the Empirical Rule.  Look it up!)

f.  The 20th percentile of Z

g. The z value with 5% area to its right.

please show all work not just answers and do all of them please and thank you will rate high

Answer 1

a) P(Z = 1.32) = 0

b) P(Z > 5) = 1 - P(Z < 5)

                  = 1 - 1 = 0

c) P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

According to the Empirical rule about 68% of the data will fall between 1 standard deviation from the mean.

d) P(-2 < Z < 2)

= P(Z < 2) - P(Z < -2)

= 0.9772 - 0.0228

= 0.9544

According to the Empirical rule about 95% of the data will fall within 2 standard deviation from the mean.

e) P(-3 < Z < 3)

= P(Z < 3) - P(Z < -3)

= 0.9987 - 0.0013

= 0.9974

According to the Empirical rule all of the data (about 99.7%) will fall within 3 standard deviation from the mean.

f) P(Z < z) = 0.2

or, z = -0.84

g) P(Z > z) = 0.05

or, 1 - P(Z < z) = 0.05

or, P(Z < z) = 0.95

or, z = 1.645