Question

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

(a)

* P*(0 ≤

(b)

* P*(−1.54 ≤

(c)

* P*(

(d)

* P*(

(e)

* P*(

(f)

* P*(

Also..

A population has a mean of 128 and a standard deviation of 32. Suppose a sample of size 64 is selected and

*x*

is 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 the population mean?

(b)

What is the probability that the sample mean will be within ±10 of the population mean?

Answer #1

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 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.

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)

1. If Z is a standard normal random variable, find the
value z0 for the following probabilities. (Round your
answers to two decimal places.)
(a) P(Z > z0) = 0.5
z0 =
(b) P(Z < z0) = 0.8686
z0 =
(c) P(−z0 < Z < z0) = 0.90
z0 =
(d) P(−z0 < Z < z0) = 0.99
z0 =
2. A company that manufactures and bottles apple juice uses a
machine that automatically fills 64-ounce bottles. There is some...

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 <= 2.73)
b) P(Z <= 1.63)
c) P(-1.05 <= Z)
d) P(|Z| <= 2.5)
How do you do this or is there an easy way you can do this in
excel?

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)

*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)

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 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)

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