Question

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.

Answer #1

Solution:

(a) P(?1.41 < z < 0.61)

P( z < 0.61) - P (z < -1.41 )

Using standard normla table

=0.7291- 0.0793

=0.6498

Probability = 0.6498

(b) P(0.55 < z < 1.78)

P( z < 1.78) - P (z <0.55 )

Using standard normla table

=0.9625- 0.7088

=0.2537

Probability = 0.2537

(c) P(?1.54 < z < ?0.44)

P( z < -0.44) - P (z <-1.54)

Using standard normla table

=0.3300 - 0.0618

=0.2628

Probability = 0.2628

(d) P(z > 1.32)

= 1 - P(z <1.32)

Using standard normla table

= 1 - 0.9066

=0.0934

Probability = 0.0934

(e) P(z < ?4.31)

Using standard normla table

= 0

Probability = 0

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) =

Given that z is a standard normal random variable, compute the
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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)

Given that z is a standard normal random variable, compute the
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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)

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decimal places):
P (0 ≤ z ≤ 0.77) =
P (-1.63 ≤ z ≤ 0) =
P (z > 0.42) =
P (z ≥ -0.22) =
P (z < 1.30) =
P (z ≤ -0.78) =

Let Z be a standard normal random variable and
calculate the following probabilities, drawing pictures wherever
appropriate. (Round your answers to four decimal
places.)
(e) P(Z ≤ 1.43)
(h) P(1.43 ≤ Z ≤
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*I'm having trouble with d.
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(-0.9 ≤ Z ≤ -0.44)
b. P(0.03 ≤ Z ≤1.5)
c. P(1.46 ≤ Z ≤ 0.05)
d. P(Z > 4)

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Find the following probabilities. (Round your answers to four
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(a) p(0 < z < 1.62)
(b) p(1.40 < z < 1.83)
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(f) p(z < 1.27)

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(a) P(X < 65)
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(c) P(58 < X <
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You may need to use the appropriate table in the Appendix of Tables
to answer this question.

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