Question

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)

Answer #1

Given that z is a standard normal random variable, compute the
following probabilities (to 4 decimals). P(-1.98 ≤ z ≤ 0.48) P(0.55
≤ z ≤ 1.29) P(-1.73 ≤ z ≤ -1.08)

Given that Z is a standard normal random variable, compute the
following probabilities (to 4 decimal places).
a. P(-1.98 ≤ z ≤ 0.49)
b. P(.55 ≤ z ≤ 1.28)
c. P(-1.79 ≤ z ≤ -1.09)

Given that z is a standard normal random variable, compute the
following probabilities. (Round your answers to four decimal
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)

Given that z is a standard normal random variable, compute the
following probabilities. Round your answers to 4 decimal
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 following probabilities. (Round your answers to four
decimal places.)(a)P(0 ≤ z ≤ 0.86)(b)P(−1.54 ≤ z ≤ 0)(c)P(z > 0.44)(d)P(z ≥ −0.22)(e)P(z < 1.30)(f)P(z ≤ −0.75)Also..A population has a mean of 128 and a standard deviation of 32.
Suppose a sample of size 64 is selected andxis used to estimate μ. (Round your answers to four
decimal places.)(a)What is the probability that the sample mean will be within ±5
of...

Given that z is a standard normal random variable, use the Excel
to compute the following probabilities.
a) P(z > 0.5)
b) P(z ≤ −1)
c) P(1≤ Z ≤ 1.5)
d) P(0.5 ≤ z ≤ 1.25)
e) P(0 < z < 2.5)

Z is a standard normal random variable. Compute the following
probabilities.
a.
P(-1.33 Z 1.67)
b.
P(1.23 Z 1.55)
c.
P(Z 2.32)
d.
P(Z -2.08)
e.
P(Z -1.08)

For standadrd normal random variable Z, find (i)
p(0 < Z < 1.35), (ii) p(-1.04 < Z < 1.45), (iii)
p(-1.40
< Z < -0.45), (iv) p(1.17 < Z < 1.45), (v) p( Z <
1.45), (vi) p(1.0 < Z < 3.45)

For the standard normal random variable z, compute the
following probabilities (if required, round your answers to four
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) =

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)

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