Question

Given that is a standard normal random variable, find for each situation (to 2 decimals). a. The area to the left of is . b. The area between 0 and is ( is positive). c. The area to the left of is . d. The area to the right of is . e. The area to the left of is . f. The area to the right of is .

Answer 1

Answer:

(a) 1.94

(b) 1.94

(c) 1.05

(d) 1.15

(e) 0.44

(f) 0.44

Step-by-step explanation:

A standard normal distribution has mean 0 and standard deviation 1.

(a)

The value of z for which P (Z < z) = 0.9738 is:

z = 1.94

(b)

Compute the value of z for which the area between 0 and z is 0.4738 as follows:

$P(0<Z<z)=0.4738\\P(Z<z)-P(Z<0)=0.4738\\P(Z<z)-0.50=0.4738\\P(Z<z)=0.9738$

The value of z is,

z = 1.94

(c)

The value of z for which P (Z < z) = 0.8531 is:

z = 1.05

(d)

The value of z for which P (Z > z) = 0.1251 is:

$P(Z>z)=0.1251\\1-P(Z<z)=0.1251\\P(Z<z)=0.8749$

z = 1.15

(e)

The value of z for which P (Z < z) = 0.67 is:

z = 0.44

(f)

The value of z for which P (Z > z) = 0.33 is:

$P(Z>z)=0.33\\1-P(Z<z)=0.33\\P(Z<z)=0.67$

z = 0.44

**Use the z-table.