In: Statistics and Probability

For a standard normal distribution, find:

P(-1.64 < z < -1.48)

We can solve this using two methods and using two different types of standard normal tables.

P(-1.64 < z < -1.48)

**METHOD 1:**

For finding P(-1.64 < z < -1.48)

we can use the standard normal table in which entries are negatives z or can be said as the entries which cover the left side of the curve which is less than the center of the curve.

The area under the curve areas:

Thus, P(-1.64 < z < -1.48) can be written as:

So, from the standard normal table, we get:

**NOTE:** *Remember we have to use the
standard normal table in which all Z entries are
negative.*

==============================================================

**METHOD 2:**

Now, we will use the standard normal table which all Z positive entries.

So,

This can be written as

Now, can be found using a formula that:

*(Total
area under the curve is equal to 1)*

So, from standard normal table

Similarly,

we can find:

So, we get:

Thus, we get:

==============================================================================

**You can use any method which you feel more
comfortable.**

Let z be a random variable with a standard normal
distribution.
Find “a” such that P(|Z| <A)= 0.95
This is what I have:
P(-A<Z<A) = 0.95
-A = -1.96
How do I use the symmetric property of normal distribution to make
A = 1.96?
My answer at the moment is P(|z|< (-1.96) = 0.95

Let z be a random variable with a standard normal distribution.
Find P(0 ≤ z ≤ 0.46), and shade the corresponding area under the
standard normal curve. (Use 4 decimal places.)

For a standard normal distribution, find
1. P(z > c)=0.3796
Find c.
2. P(z < c)=0.0257
Find c.
3. P(-2.68< z > -0.38)
4. P(z > -1.55)
5. P(z < -0.32)

For a standard normal distribution, find:
P(z < c) = 0.0414
Find c rounded to two decimal places.

For a standard normal distribution, find:
P(z < -0.64)
Express the probability as a decimal rounded to 4 decimal
places.

Find the following probabilities for the standard normal random
variable z z :
a) P(−2.07≤z≤1.93)= P ( − 2.07 ≤ z ≤ 1.93 ) =
(b) P(−0.46≤z≤1.73)= P ( − 0.46 ≤ z ≤ 1.73 ) =
(c) P(z≤1.44)= P ( z ≤ 1.44 ) =
(d) P(z>−1.57)= P ( z > − 1.57 ) =

A) If Z is standard normal, then P(Z < 0.5) is

Find the area under the standard normal distribution curve:
a) Between z = 0 and z = 1.95
b) To the right of z = 1.99
c) To the left of z = -2.09
How would I do this?

Find the area under the standard normal distribution curve:
a) Between z = 0 and z = 1.95
b) To the right of z = 1.99
c) To the left of z = -2.09
How would I do this?

QUESTION 5
The variable Z has a standard normal distribution. The
probability P(- 0.5 < Z < 1.0) is:
a.
0.5328
b.
0.3085
c.
0.8413
d.
0.5794
QUESTION 6
If a random variable X is normally distributed with a mean of 30
and a standard deviation of 10, then P(X=20) =
a.
0.4772
b.
-0.4772
c.
-2.00
d.
0.00
QUESTION 7
If P( -z < Z < +z) = 0.8812, then the z-score is:
a.
1.56
b.
1.89
c.
0.80...

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