Question

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.)

Answer #1

a) P( Z > 1.32) = 1- P( Z < 1.32)

= 1- 0.90658

=**0.09342**

b) P( Z < -1.96)= 1- P( Z < 1.96)

= 1- 0.97500

= **0.025**

c) P(0.69 ≤ Z ≤ 2.59)= P( Z <2.59) - P( Z < 0.69)

= 0.99520 - 0.75490

= **0.2403**

d)P( -1.79 ≤ Z< -0.61)= P( z < -0.61) - P( z < -1.79)

= [ 1- P(z < 0.61)] - [ 1- P( z < 1.79)]

= P( z < 1.79) - P( z < 0.61)

= 0.96327 - 0.72907

= **0.2342**

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

= 1- 0.5

= **0.5**

f) P( -2.52 ≤ Z ≤ 1.01 )= P( z < 1.01) - P( z < -2.52)

= P( z < 1.01) -[1- P( z < 2.52)]

= P( z < 1.01) - 1 + P( z < 2.52)

= 0.84375 - 1 + 0.99413

= **0.83788**

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 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.)

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 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
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four decimal places.)
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