Question

Let Z be the standard normal variable. Find the values of z if z satisfies the given probabilities. (Round your answers to two decimal places.) (a) P(Z > z) = 0.9678 z =

(b) P(−z < Z < z) = 0.7888 z =

Answer #1

a) We want to find, the z-score such that, P(Z > z) = 0.9678

P(Z > z) = 0.9678

=> 1 - P(Z < z) = 0.9678

=> P(Z < z) = 1 - 0.9678

=> P(Z < z) = 0.0322

Using standard normal z-table we get, z-score corresponding
probability of 0.0322 is, z =
**-1****.85**

=> P(Z > **-1.85)** = 0.9678

**=> Z = -1.85**

b) We want to find, the z-score such that, P(-z < Z < z) = 0.7888

P(-z < Z < z) = 0.7888

=> 2 * P(Z < z) - 1 = 0.7888

=> 2 * P(Z < z) = 1.7888

=> P(Z < z) = 1.7888/2

=> P(Z < z) = 0.8944

Using standard normal z-table we get z-score corresponding
probability of 0.8944 is, z = **1.25**

=> P(-1.25 < Z < 1.25) = 0.7888

=> Z = **1.25**

Let "Z" be a random variable from the standard normal
distribution. Find the value for ? that satisfies each of
the following probabilities.
(Round all answers to two decimal places)
A) P(Z < ?) = 0.6829.
? =
B) P(Z > ?) = 0.3087.
? =
C) P(-? < Z < ?) =
0.7402.
? = ±

Find the following z values for the standard normal
variable Z. (Negative values should be indicated
by a minus sign. Round your answers to 2 decimal
places.)
a.
P(Z ≤
z) = 0.9477
b.
P(Z >
z) = 0.6300
c.
P(−z ≤
Z ≤ z) = 0.85
d.
P(0 ≤ Z ≤
z) = 0.2034

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)

A: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(z ≤ 1.11) =
B: 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) =
C: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−1.78 ≤ z...

Find the following z values for the standard normal
variable Z. (You may find it
useful to reference the
z table.Negative values should be
indicated by a minus sign. Round your answers to 3 decimal
places.)
a.
P(Z ≤ z)
= 0.1022
b.
P(z ≤ Z ≤
0) = 0.1641
c.
P(Z > z ) = 0.9719
d.
P(0.29 ≤ Z ≤ z) = 0.3777

Find the following z values for the standard normal variable Z.
(You may find it useful to reference the z table. Negative values
should be indicated by a minus sign. Round your answers to 3
decimal places.)
a. P(Z ≤ z) = 0.1065
b. P(z ≤ Z ≤ 0) = 0.1746
c. P(Z > z ) = 0.9412
d. P(0.4 ≤ Z ≤ z) = 0.3177

Use Table A to find the value z of a standard Normal variable
that satisfies each of the following conditions. (Use the value of
z from Table A that comes closest to satisfying the condition.) In
each case, sketch a standard Normal curve with your value of z
marked on the axis. (Round your answers to two decimal places.)
(a) The point z with 60% of the observations falling below
it
(b) The point z with 17% of the observations...

Find the following z values for the standard normal
variable Z. Use Table 1. (Negative values should
be indicated by a minus sign. Round your answers to 2 decimal
places.)
a.
P(Z ≤
z) = 0.9478
b.
P(Z >
z) = 0.6140
c.
P(−z ≤
Z ≤ z) = 0.80
d.
P(0 ≤ Z ≤
z) = 0.2392
Hints

Find the following z values for the standard normal variable Z.
(You may find it useful to reference the z table. Negative values
should be indicated by a minus sign. Round your answers to 2
decimal places.)
a. P(Z ≤ z) = 0.9478
b. P(Z > z) = 0.6321
c. P(-z ≤ Z ≤ z ) = 0.88
d. P( 0 ≤ Z ≤ z) = 0.3232
Please show work, thank you.

Find the following z values for the standard normal variable Z.
(Use Excel command instead of the z table. Negative values should
be indicated by a minus sign. Round your answers to 2 decimal
places.)
a.
P(Z ≤ z) = 0.9477
b.
P(Z > z) = 0.63
c.
P(−z ≤ Z ≤ z) = 0.85
d.
P(0 ≤ Z ≤ z) = 0.2034

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