Question

Find a value of the standard normal random variable z , call it

z 0z0,

such that the following probabilities are satisfied.

a.
P(zless than or equals≤z 0z0)equals=0.04360.0436 |
e.
P(minus−z 0z0less than or equals≤zless than or equals≤0)equals=0.28492849 |

b.
P(minus−z 0z0less than or equals≤zless than or equals≤z 0z0)equals=0.9090 |
f.
P(minus−33less than<zless than<z 0z0)equals=0.96009600 |

c.
P(minus−z 0z0less than or equals≤zless than or equals≤z 0z0)equals=0.9595 |
g.
P(zgreater than>z 0z0)equals=0.5 |

d.
P(minus−z 0z0less than or equals≤zless than or equals≤z 0z0)equals=0.82468246 |
h.
P(zless than or equals≤z 0z0)equals=0.0062 |

Answer #1

Refer Standard normal table or Z-table, Lookup for Z-value
corresponding to area 0.0436 to the left of the normal *or use
excel formula
"***=NORM.S.INV(**0.0436**)***" to
find the Z-value* curve.

----------------------------------------------------------------------------------------------------

Refer Standard normal table or Z-table, Lookup for Z-value
corresponding to area 0.95 to the left of the normal curve *or
use excel formula
"***=NORM.S.INV(**0.95**)***" to
find the Z-value* curve.

----------------------------------------------------------------------------------------------------

Refer Standard normal table or Z-table, Lookup for Z-value
corresponding to area 0.975 to the left of the normal curve *or
use excel formula
"***=NORM.S.INV(**0.975**)***" to
find the Z-value* curve.

----------------------------------------------------------------------------------------------------

Refer Standard normal table or Z-table, Lookup for Z-value
corresponding to area 0.9123 to the left of the normal curve *or
use excel formula
"***=NORM.S.INV(**0.9123**)***" to
find the Z-value* curve.

----------------------------------------------------------------------------------------------------

*Refer Z-table to find the probability or use excel formula
"=NORM.S.DIST(0, TRUE)" to find the probability.*

*Refer Z-table, Lookup for Z-value corresponding to area
0.7849 to the left of the normal curve or use excel formula
"***=NORM.S.INV(***0.7849***)***"
to find the Z-value.*

----------------------------------------------------------------------------------------------------

*Refer Z-table to find the probability or use excel formula
"=NORM.S.DIST(-3, TRUE)" to find the probability.*

*Refer Z-table, Lookup for Z-value corresponding to area
0.9613 to the left of the normal curve or use excel formula
"***=NORM.S.INV(***0.9613***)***"
to find the Z-value.*

----------------------------------------------------------------------------------------------------

*Refer Z-table, Lookup for Z-value corresponding to area 0.5
to the left of the normal curve or use excel formula
"***=NORM.S.INV(0.5)***" to find the
Z-value.*

----------------------------------------------------------------------------------------------------

Refer Standard normal table or Z-table, Lookup for Z-value
corresponding to area 0.0062 to the left of the normal *or use
excel formula
"***=NORM.S.INV(**0.0062**)***" to
find the Z-value* curve.

Find the following probability for the standard normal random
variable z.
a.
P(zgreater than>1.981.98)
e.
P(zgreater than or equals≥0)
b.
P(zless than<negative 1.64−1.64)
f.
P(negative 2.72−2.72less than or equals≤zless than or
equals≤1.531.53)
c.
P(0.170.17less than or equals≤zless than or
equals≤2.122.12)
g.
P(zgreater than or equals≥negative 2.63−2.63)
d.
P(negative 1.25−1.25less than or equals≤zless than<negative
0.65−0.65)
h.
P(zless than<2.632.63)

Find the following probability for the standard normal random
variable z.
a.
P(zgreater than>1.381.38)
e.
P(zgreater than>0)
b.
P(zless than<negative 1.11−1.11)
f.
P(negative 2.31−2.31less than or equals≤zless than or
equals≤1.331.33)
c.
P(0.680.68less than or equals≤zless than or
equals≤2.412.41)
g.
P(zgreater than or equals≥negative 2.64−2.64)
d.
P(negative 1.18−1.18less than or equals≤zless than<negative
0.52−0.52)
h.
P(zless than<2.642.64)

Find these probabilities for a standard normal random variable
Z. Be sure to draw a picture to check your calculations. Use the
normal table or software.
(a)
P(Zless than<1.11.1)
(d)
P(StartAbsoluteValue Upper Z EndAbsoluteValueZgreater
than>0.40.4)
(b)
P(Zgreater than>negative 1.4−1.4)
(e)
P(negative 1.4−1.4less than or equals≤Zless than or
equals≤1.11.1)
(c)
P(StartAbsoluteValue Upper Z EndAbsoluteValueZless
than<1.61.6)

Find the following probability for the standard normal random
variable z.
a.
P(zgreater than>1.321.32)
d.
P(negative 1.79−1.79less than or equals≤zless than<negative
0.61−0.61)
b.
P(zless than<negative 1.96−1.96)
e.
P(zgreater than>0)
c.
P(0.690.69less than or equals≤zless than or
equals≤2.592.59)
f.
P(negative 2.52−2.52less than or equals≤zless than or
equals≤1.011.01)
(Round to three decimal places as needed.)

Please show work and calculations! thank you!
Find a value of the standard normal random variable z , call it
z0, such that the following probabilities are satisfied.
P( -2 < z < z0) = 0.9607

Given that z is a standard normal random variable, use the Excel
to compute the following probabilities.
a) P(z > 0.5)
b) P(z ≤ −1)
c) P(1≤ Z ≤ 1.5)
d) P(0.5 ≤ z ≤ 1.25)
e) P(0 < z < 2.5)

Please show formula and work and calculations! thank you!
Find a value of the standard normal random variable z , call it
z0, such that the following probabilities are satisfied.
a. P( - z0 ≤ z ≤ 0) = 0.2612
b. P( -3 < z < z0) = 0.9559

Find the value of the standard normal random variable z,called
z0 such that: (a) P(Z≤z0) = 0.8483 z0 = (b) P(−z0 ≤Z≤z0) = 0.9444
z0 = (c) P(−z0 ≤Z≤z0) = 0.161 z0 = (d) P(Z≥z0) = 0.4765 z0 = (e)
P(−z0 ≤Z≤0) = 0.0792 z0 = (f) P(−1.76≤Z≤z0) = 0.7304 z0 =

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 value of the standard normal random variable z, called
z0 such that:
(a) P(z≤z0)=0.9589
z0=
(b) P(−z0≤z≤z0)=0.0602
z0=
(c) P(−z0≤z≤z0)=0.6274
z0=
(d) P(z≥z0)=0.2932
z0=
(e) P(−z0≤z≤0)=0.4373
z0=
(f) P(−1.38≤z≤z0)=0.8340
z0=

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