Question

For the standard normal random variable *z*, find
*z* for each situation. If required, round your answers to
two decimal places. For those boxes in which you must enter
subtractive or negative numbers use a minus sign. (Example:
-300)'

a. The area to the left of *z* is 0.1827. *z*
=

b. The area between −*z* and *z* is 0.9830.
*z* =

c. The area between −*z* and *z* is 0.2148.
*z* =

d. The area to the left of *z* is 0.9997. *z*
=

e. The area to the right of *z* is 0.6847.
*z*=

Answer #1

Solution :

Using standard normal table,

a)

P(Z < z) = 0.1827

P(Z < -0.91) = 0.1827

z = -0.91

(b)

P(-z < Z < z) = 0.9830

P(Z < z) - P(Z < z) = 0.9830

2P(Z < z) - 1 = 0.9830

2P(Z < z) = 1 + 0.9830

2P(Z < z) = 1.9830

P(Z < z) = 1.9830 / 2 = 0.9915

P(Z < 2.39) = 0.9915

z = 2.39

(c)

P(-z < Z < z) = 0.2148

P(Z < z) - P(Z < z) = 0.2148

2P(Z < z) - 1 = 0.2148

2P(Z < z) = 1 + 0.2148

2P(Z < z) = 1.2148

P(Z < z) = 1.2148 / 2

P(Z < 0.27) = 0.6074

z = 0.27

d)

P(Z < z) =0.9997

P(Z < 3.43) = 0.9997

z = 3.43

e)

P(Z > z) = 0.6847

1 - P(Z < z) = 0.6847

P(Z < z) = 1 - 0.6847 = 0.3153

P(Z < -0.48) = 0.3153

z = -0.48

Can someone show the work on how to do this?
Thanks!
---------
For the standard normal random variable z, find
z for each situation. If required, round your answers to
two decimal places. For those boxes in which you must enter
subtractive or negative numbers use a minus sign. (Example:
-300)
The area to the left of z is 0.2119. z
=
The area between −z and z is 0.9030.
z =
The area between −z and z is 0.2052....

Given that z is a standard normal random variable, find z for
each situation.
(a) The area to the left of z is 0.2743.
(b) The area between −z and z is 0.9534.
(c) The area between −z and z is 0.2052. (
d) The area to the left of z is 0.9951.
(e) The area to the right of z is 0.6915.

Given that z is a standard normal random variable, find z for
each situation (to 2 decimals)
a. the area to the left of z is 0.9732
b. the area between 0 and z is 0.4732
c. the area to the left of z is 0.8643
d. the area to the right of z is 0.1251
e. the are to the left of z is 0.6915
f. the are to the right of z is 0.3085

Given that z is a standard normal random variable, find z for
each situation. (Round your answers to two decimal places.) (a) The
area to the right of z is 0.01. (b) The area to the right of z is
0.025. (c) The area to the right of z is 0.05. (d) The area to the
right of z is 0.10.

Given that z is a standard normal random variable, find z for
each situation (to 2 decimals).
A. The area to the left of z is 0.209.
B. The area between -z and z is 0.905.
C. The area between -z and z is 0.2052.
D. The area to the left of z is 0.9951.
E. The area to the right of z is 0.695.

Given that z is a standard normal random variable,
find for each situation (to 2 decimals).
a. The area to the left of z is .9772.
b. The area between 0 and z is .4772 ( z is
positive).
c. The area to the left of z is .8729.
d. The area to the right of z is .1170.
e. The area to the left of z is .6915.
f. The area to the right of z is .3085

Given that z is a Standard Normal random variable, find z for
each situation:
(9 marks)
the area to the left of z is 0.68
the area to the right of z is 0.68
the total area to the left of –z and to the right of z is
0.32

Find the value of the standard normal random variable z, called
z0, for each situation. Your answer should be correct to within
0.01 (as discussed in class).
(a) Area to the left is 0.63 z0=
(b) Area to the left is 0.71 z0=
(c) Area to the right is 0.49 z0=
(d) Area to the right is 0.18 z0=

6. Suppose z is a standard normal variable. Find the
value of z in the following.
a.
The area between 0 and z is .4678.
b.
The area to the right of z is .1112.
c.
The area to the left of z is .8554
d.
The area between –z and z is .754.
e.
The area to the left of –z is .0681.
f.
The area to the right of –z is .9803.

For the standard normal random variable z, compute the
following probabilities (if required, round your answers to four
decimal places):
P (0 ≤ z ≤ 0.77) =
P (-1.63 ≤ z ≤ 0) =
P (z > 0.42) =
P (z ≥ -0.22) =
P (z < 1.30) =
P (z ≤ -0.78) =

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