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 (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 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) =

Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Enter a number.
Round your answer to four decimal places.)
P(z ≥ 1.41) =
Sketch the area under the standard normal curve over the
indicated interval and find the specified area. (Enter a number.
Round your answer to four decimal places.)
The area between z = 0.41 and z = 1.82 is
.

Let z be a random variable with a standard normal distribution.
Find the indicated probability. (Round your answer to four decimal
places.) P(z ? ?0.25)
Let z be a random variable with a standard normal distribution.
Find the indicated probability. (Round your answer to four decimal
places.) P(z ? 1.24)
Let z be a random variable with a standard normal distribution.
Find the indicated probability. (Enter your answer to four decimal
places.) P(?2.20 ? z ? 1.08)

Find the following probabilities for the standard normal random
variable z. (Round your answers to four decimal places.)
(a) P(−1.43 < z < 0.64) =
(b) P(0.52 < z < 1.75) =
(c) P(−1.56 < z < −0.48) =
(d) P(z > 1.39) =
(e) P(z < −4.34) =

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