Question

1) Find the following probabilities:

a) Pr{Z < 0.63}

b)Pr{Z ≥ −0.63}

c) Pr{−2.12 < Z < 2.12}

d) Pr{−2.12 < Z < 0.0}

e) Pr{−4.00 < Z < 0.0}

f) Pr{Z < −1.32 or Z > 1.32} (you want the probability that Z
is outside the range −1.32 to 1.32)

g) Pr{−1.32 < Z < 1.32} h) Add (f) and (g). Are you surprised? Why or why not?

Answer #1

a)

P(z < 0.63) = **0.7357**

b)

P(Z >= -0.63) = P(Z < 0.63)

= **0.7357**

c)

P(-2.12 < Z < 2.12) = P(Z < 2.12) - P(Z < -2.12)

= 0.9830 - 0.0170

= **0.9660**

d)

P( -2.12 < Z < 0) = P(Z < 0) - P(Z < -2.12)

= 0.5 - 0.0170

= **0.4830**

e)

P(-4 < Z < 0) = P(Z < 0) - P(Z < -4.00)

= 0.5 - 0

= **0.5**

f)

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

= 1 - [ P(Z < 1.32) - P(Z < -1.32) ]

= 1 - [ 0.9066 - 0.0934 ]

= **0.1868**

g)

P( -1.32 < Z < 1.32) = P(Z < 1.32) - P(Z < -1.32)

= 0.9066 - 0.0934

= **0.8132**

h)

f + g = 0.1868 + 0.8132

= 1

yes, Since total area between z-score of -1.32 and z-score of 1.32 and outside of -1.32 and 1.32 is

whole area of the curve.

It should be 1.

a) Pr{Z < 0.63}
b) Pr{Z ≥ −0.63}
c) Pr{−2.12 < Z < 2.12}
d) Pr{−2.12 < Z < 0.0}
e) Pr{−4.00 < Z < 0.0}
f) Pr{Z < −1.32 or Z > 1.32} (you want the probability
that Z is outside the range −1.32 to 1.32)
g) Pr{−1.32 < Z < 1.32}
h) Add (f) and (g). Are you surprised? Why or why not?

Find the following probabilities:
a) Pr{Z < 0.33}
b) Pr{Z ≥ −0.33}
c) Pr{−2.06 < Z < 2.06}
d) Pr{−2.06 < Z < 0.0}
e) Pr{−4.00 < Z < 0.0}
f) Pr{Z < −1.75 or Z > 1.75} (you want the probability that Z
is outside the range −1.75 to 1.75) g) Pr{−1.75 < Z <
1.75}

Find the following probabilities: Please show
work
a) Pr{Z < 0.33}
b) Pr{Z ≥ -0.33}
c) Pr{-1.67 < Z < 1.67}
d) Pr{-2.91 < Z < 0.0}
e) Pr{Z < -1.03 or Z > 1.03}
(you want the probability that Z is outside the range -1.03 to
1.03)

1) Find the following probabilities: a) Pr{Z < 0.67} b) Pr{Z
≥ -0.67} c) Pr{-2.05 < Z < 2.05} d) Pr{-2.91 < Z <
0.31} e) Pr{Z < -2.03 or Z > 2.03} (you want the probability
that Z is outside the range -3.03 to 3.03)
2) Assuming that for the height of women, μ = 65.2 inches and σ
= 2.9 inches, find the following: a) Pr{Y > 65.7} b) Pr{Y <
57.8} c) Pr{60 < Y < 69}...

Find the following probabilities. (Round your answers to four
decimal places.)
(a) p(0 < z < 1.62)
(b) p(1.40 < z < 1.83)
(c) p(−0.38 < z < 1.55)
(d) p(z < −1.91)
(e) p(−1.32 < z < −0.86)
(f) p(z < 1.27)

Find the following probabilities:
a. P (z > 1.96)
b. P (z > .96)
c. P (z > 3.00)
d. P (z < 1.96)
e. P (z < .49)

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.

Calculate the following probabilities using the standard normal
distribution. (Round your answers to four decimal places.)
(a)
P(0.0 ≤ Z ≤ 1.6)
(b)
P(−0.1 ≤ Z ≤ 0.0)
(c)
P(0.0 ≤ Z ≤ 1.49)
(d)
P(0.6 ≤ Z ≤ 1.51)
(e)
P(−2.05 ≤ Z ≤ −1.76)
(f)
P(−0.02 ≤ Z ≤ 3.54)
(g)
P(Z ≥ 2.60)
(h)
P(Z ≤ 1.66)
(i)
P(Z ≥ 6)
(j)
P(Z ≥ −8)

Find the following probabilities. (Round your answers to four
decimal places.)
(a) p(0 < z < 1.42)
(b) p(1.02 < z < 1.65)
(c) p(−0.88 < z < 1.72)
(d) p(z < −2.09)
(e) p(−2.35 < z < −1.19)
(f) p(z < 1.51)

Please answer all the question or i wont rate your answer. Thank
you
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 ≤ 2.22)
(b) P(0 ≤ Z ≤ 2)
(c) P(−2.60 ≤ Z ≤ 0)
(d) P(−2.60 ≤
Z ≤ 2.60)
(e) P(Z ≤ 1.32)
(f) P(−1.05 ≤ Z)
(g) P(−1.60 ≤ Z ≤ 2.00)
(h) P(1.32 ≤ Z ≤
2.50)
(i) P(1.60 ≤ Z)
(j) P(|Z| ≤ 2.50)

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