Question

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) |

Answer #1

a)

P(Z > 1.98) = 1 - P(Z < 1.98)

= 1 - 0.9761(From Z table)

= **0.0239**

b)

P(Z < -1.64) = 1 - P(Z < 1.64)

= 1 - 0.9495 (From Z table)

= **0.0505**

c)

0.17 <= Z <= 2.12) = P(Z <= 2.12) - P(Z <= 0.17)

= 0.9830 - 0.5675 (From Z table)

= **0.4155**

d)

P(-1.25 <= Z <= -0.65) = P(Z <= -0.65) - P(Z <= -1.25)

= ( 1 - P(Z < 0.65) ) - ( 1 - P(Z < 1.25) )

= ( 1 - 0.7422) - ( 1 - 0.8944) (From Z table)

= **0.1522**

e)

P(Z >= 0) = 1 - P(Z < 0)

= 1 - 0.5 (From Z table)

= **0.5**

f)

P(-2.72 <= Z <= 1.53) = P(Z < 1.53) - P(Z < -2.72)

P(Z < 1.53) - ( 1 - P(Z < 2.72) )

= 0.9370 - ( 1 - 0.9967 ) (From Z table)

= **0.9337**

g)

P(Z >= - 2.63) = P(Z < 2.63)

= **0.9957**(From Z table)

h)

P(Z < 2.63) = **0.9957** (From Z table)

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 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.)

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...

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 indicated probability using the standard normal
distribution.
P(zless than<negative 1.71−1.71orzgreater
than>1.711.71)
P(zless than<negative 1.71−1.71or zgreater
than>1.711.71)equals=nothing
(Round to four decimal places as needed.)

Answer the following questions about the standard normal random
variable Z. (Use 4 decimal places in your answers to parts a.
through f.)
a. What is P(-1.55 < Z < 0.61)?
b. What is P(0 < Z < 1.33)?
c. What is P(Z > -1.72)?
d. What is P(Z < -2.7)?
e. What is P(Z < 2.63)?
f. What is P(-2.57 < Z < -1.22)?

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 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 =

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)

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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