Question

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) |

Answer #1

a) P(Z < 1.1) = 0.8643

b) P(Z > -1.4) = 1 - P(Z < -1.4) = 1 - 0.0808 = 0.9192

c) P(|Z| < 1.6) = P(-1.6 < Z < 1.6) = P(Z < 1.6) - P(Z < -1.6) = 0.9452 - 0.0548 = 0.8904

d) P(|Z| > 0.4) = 1 - P(|Z| < 0.4) = 1 - P(-0.4 < Z < 0.4) = 1 - (P(Z < 0.4) - P(Z < -0.4)) = 1 - (0.6554 - 0.3446) = 0.6892

e) P(-1.4 < Z < 1.1) = P(Z < 1.1) - P(Z < -1.4) = 0.8643 - 0.0808 = 0.7835

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 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...

Given that Z is a standard normal random variable, compute the
following probabilities. Draw a curve and shade appropriate region.
Use TI-83 calculator to find the probabilities
(i) P( z ≤ 1.0)
(ii) P( z ³ 1.0)
(iii) P( z ≤ -1.0)
(iv) P(-1.0 ≤ z ≤ 1.0)
(v) P(-1.6 ≤ z ≤ 1.2)

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)

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(?1.41 < 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 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 the following probabilities.
Draw a picture of the normal curve and shade the area :
1. P (z ≤ 1.31) =
2. P (z ≥ 1.65) =
3. P (−2.17 ≤ z ≤ 2.18) =

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