Question

Find the probabilities associated with the standard normal random variable Z:

a) P (Z> 2.54)

b) P (-3.2 <Z <3.2)

c) P (Z <1.94)

d) P (Z> 2.88)

e) P (Z> 3.15)

Answer #1

a) P (Z> 2.54)

Probability= 0.9945 (using standard normal table)

b) P(-3.2 <Z <3.2)

= P(Z <3.2) - P(Z < -3.2)

= 0.9993 - 0.0007

Probability= 0.9986

c) P (Z <1.94)

Probability= 0.9738

d) P (Z> 2.88)

Probability= 0.9980

e) P (Z> 3.15)

Probability= 0.9992

Z is a standard normal random variable. Compute the following
probabilities.
a.
P(-1.33 Z 1.67)
b.
P(1.23 Z 1.55)
c.
P(Z 2.32)
d.
P(Z -2.08)
e.
P(Z -1.08)

Find the following probabilities for a standard normal random
variable z : p(z > 1.53) with steps

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) =

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 probabilities for the standard normal random
variable z. (Round your answers to four decimal
places.)
(a) P(?1.41 < z < 0.61) =
(b) P(0.55 < z < 1.78) =
(c) P(?1.54 < z < ?0.44) =
(d) P(z > 1.32) =
(e) P(z < ?4.31) =
You may need to use the appropriate appendix table or technology to
answer this question.

Find the following probabilities based on the standard normal
variable Z. (You may find it useful to reference
the z table. Leave no cells blank
- be certain to enter "0" wherever required. Round your answers to
4 decimal places.)
a.
P(−1.01 ≤ Z ≤ −0.71)
b.
P(0.01 ≤ Z ≤ 2.45)
c.
P(−1.38 ≤ Z ≤ 0.06)
d.
P(Z > 3.2)

Let z denote a standard normal random variable.
a. Find P(z > 1.48).
b. Find P(-0.44 < z < 2.68).
c. Determine the value of which
satisfies P(z > z. ) = 0.7995. d. Find P(z <
–0.87).

Given that z is a standard normal random variable, compute the
following probabilities. (Round your answers to four decimal
places.)
(a)
P(z ≤ −3.0)
(b)
P(z ≥ −3)
(c)
P(z ≥ −1.3)
(d)
P(−2.4 ≤ z)
(e)
P(−1 < z ≤ 0)

Given that z is a standard normal random variable, compute the
following probabilities. Round your answers to 4 decimal
places.
a. P(0 _< z _< 0.51)
b. P( -1.61 _< z _< 0)
c. P( z > 0.30)
d. P( z _> -0.31)
e. P( z < 2.06)
f. P( z _< -0.61)

-. For what follows, Z denotes the standard normal random
variable.
(1) P(Z<1.26) is about
(a) 0.7924
(b) 0.3962
(c) 0.1038
(d) 0.6038
(e) 0.8962
(2) P(-0.54 < Z < 0.78) is about
(a) 0.2054
(b) 0.0769
(c) 0.4877
(d) 0.2823
(e) 0.6877
-Assume the random variable X is normally distributed with mean
172 and standard deviation 10. Find the following
probabilities.
(3) P(X<160)
(a) 0.8849
(b) 0.1151
(c) 0.9999
(d) 0.8078
(e) 0.8438
(4) P(X>150)
(a) 0.0139
(b) 0.9861...

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