Question

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.1) = (b) P(z < -0.1) = (c) P(0.40 < z < 0.84) = (d) P(-0.84 < z < -0.40) = (e) P(-0.40 < z < 0.84) = (f) P(z > -1.25) = (g) P(z < -1.51 or z > 2.50) =

Answer #1

Part a)

P ( Z < 0.1 ) = 0.5398

Part b)

P ( Z < -0.1 ) = 0.4602

Part c)

P ( 0.4 < Z < 0.84 ) = P ( Z < 0.84 ) - P ( Z < 0.4
)

P ( 0.4 < Z < 0.84 ) = 0.7995 - 0.6554

P ( 0.4 < Z < 0.84 ) = 0.1441

part d)

P ( -0.84 < Z < -0.4 ) = P ( Z < -0.4 ) - P ( Z < -0.84
)

P ( -0.84 < Z < -0.4 ) = 0.3446 - 0.2005

P ( -0.84 < Z < -0.4 ) = 0.1441

Part e)

P ( -0.4 < Z < 0.84 ) = P ( Z < 0.84 ) - P ( Z < -0.4
)

P ( -0.4 < Z < 0.84 ) = 0.7995 - 0.3446

P ( -0.4 < Z < 0.84 ) = 0.455

Part f)

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

P ( Z > -1.25 ) = 1 - 0.1056

P ( Z > -1.25 ) = 0.8944

Part g)

P ( -1.51 < Z < 2.5 ) = P ( Z < 2.5 ) - P ( Z < -1.51
)

P ( -1.51 < Z < 2.5 ) = 0.9938 - 0.0655

P ( -1.51 < Z < 2.5 ) = 0.9283

Required probability = 1 - 0.9283 = 0.0717

Let z denote a random variable having a normal
distribution with μ = 0 and σ = 1. Determine each
of the probabilities below. (Round all answers to four decimal
places.)
(a) P(z < 0.1) =
(b) P(z < -0.1) =
(c) P(0.40 < z < 0.85) =
(d) P(-0.85 < z < -0.40)
=
(e) P(-0.40 < z < 0.85) =
(f) P(z > -1.26) =
(g) P(z < -1.49 or z > 2.50) =

1. Let z denote a random variable having a normal
distribution with μ = 0 and σ = 1. Determine each of the following
probabilities. (Round all answers to four decimal places.)
(c) P(0.40 < z < 0.85)
=
(d) P(−0.85 < z < −0.40)
=
(e) P(−0.40 < z < 0.85)
=
2. Three friends (A, B, and C) will participate in a round-robin
tournament in which each one plays both of the others. Suppose
that
P(A beats B)...

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...

Let Z be a standard normal random variable and calculate the
following probabilities, drawing pictures wherever appropriate.
(Round your answers to four decimal places.)
(a) P(0 ≤ Z ≤ 2.57)
(b) P(0 ≤ Z ≤ 2)
(c) P(−2.80 ≤ Z ≤ 0)
(d) P(−2.80 ≤ Z ≤ 2.80)
(e) P(Z ≤ 1.14)
(f) P(−1.45 ≤ Z)
(g) P(−1.80 ≤ Z ≤ 2.00)
(h) P(1.14 ≤ Z ≤ 2.50)
(i) P(1.80 ≤ Z)
(j) P(|Z| ≤ 2.50)

Consider a standard normal random variable with μ = 0 and
standard deviation σ = 1. (Round your answers to four decimal
places.)
P(z < 2) =
P(z > 1.17) =
P(−2.34 < z < 2.34) =
P(z < 1.86) =

Let z denote a variable that has a standard normal
distribution. Determine the value z* to satisfy the
following conditions. (Round all answers to two decimal
places.)
(a) P(z < z*) = 0.0256
z* =
(b) P(z < z*) = 0.0097
z* =
(c) P(z < z*) = 0.0484
z* =
(d) P(z > z*) = 0.0204
z* =
(e) P(z > z*) = 0.0097
z* =
(f) P(z > z* or z <
−z*) = 0.2007
z* =

Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−1.21 ≤ z ≤ 2.50) =
P(−2.20 ≤ z ≤ 1.08) =
P(−2.08 ≤ z ≤ −0.30) =
P(0 ≤ z ≤ 1.62) =
P(−2.22 ≤ z ≤ 0) =
P(−0.45 ≤ z ≤ 2.04) =

Let Z be a standard normal random variable (mean = 0
and sd = 1) and calculate the following probabilities:
(a) Pr(0 ≤ Z ≤
2.49)
(b) Pr(0 ≤ Z ≤ 1)
(c)
Pr(−2.50 ≤ Z ≤ 0)
(d)
Pr(−2.50 ≤ Z ≤ 2.50)
(e) Pr(Z ≤ 1.52)

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 ≤
2.50)

Let "Z" be a random variable from the standard normal
distribution. Find the value for ? that satisfies each of
the following probabilities.
(Round all answers to two decimal places)
A) P(Z < ?) = 0.6829.
? =
B) P(Z > ?) = 0.3087.
? =
C) P(-? < Z < ?) =
0.7402.
? = ±

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