Question

Use the table of standard normal probabilities (z table) to answer the following questions. Please explain how you calculate.

- What is P(z >2.5)?
- What is P(-0.8 < z < 1.5)?
- What is P(0.65< z < 1.36)?
- What z-value leaves 80 % of the normal distribution to its right?
- What z-value, and its negative, leaves 10 % of the normal distribution in each tail (a total of 20% of the distribution in both tails combined)?

Answer #1

stands for cumulative standard normal distribution.

a) The probability,

(Look up the standard normal table for z=-2.5)

b) The probability,

c) The probability,

d) We need to find the 20-th percentile of standard normal distribution.

e) We need to find the 90-th percentile of standard normal distribution.

The required z-value is

4. Find each of the following
probabilities (P) for a normal distribution.
A. P (z
> -1.00)
B. P (z > -0.80)
C. P (z
< 0.25)
5. For a normal distribution, identify
the z-score value(s) that separate the area of the distribution
into sections so that there is…
A. 80% on
the right, and 20% on the left
B. 90% in
the middle, and 5% on each side
C. 95% in
the middle, and...

. Standard Normal Table. Answer the following questions relating
to standard normal probabilities by using the table. Sketch the
bell-curve showing appropriate Z-scores, and shaded areas. Show any
operations taken such as subtractions, when answer does not come
directly from table.
(a) P(Z > −1.65)
(b) P(Z < 1.28)
(c) P(1.28 < Z < 2.05)
(d) Z-score, a, such that P(Z < a) = .0060
(e) Z-score, b, such that P(−b < Z < b) = .7500

please answer all
1.) Use Table A to find the value z of a standard
Normal variable that satisfies each of the following conditions.
(Use the value of z from Table A that comes closest to
satisfying the condition.) In each case, sketch a standard Normal
curve with your value of z marked on the axis. (Round your
answers to two decimal places.)
(a) The point z with 64% of the observations falling
below it
z =
(b) The point...

Find the following probabilities based on the standard normal
variable Z. (Use Excel to get the
probabilities. Round your answers to 4 decimal
places.)
a.
P(Z > 1.12)
b.
P(Z ≤ −2.35)
c.
P(0 ≤ Z ≤ 1.34)
d.
P(−0.8 ≤ Z ≤ 2.44)

Which of the following accurately describes the proportions of
scores in the tails of a normal distribution? A. Proportions in the
right-hand tail are positive, and proportions in the left-hand tail
are negative. B. Proportions in the right-hand tail are negative,
and proportions in the left-hand tail are positive. C. Proportions
in both tails are positive (i.e., the value of proportion is always
a positive number) D. Proportions in both tails are negative.

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)

Question 2. Look up the probabilities from the standard normal
distribution table for the following z-scores: a. z=1.96 b. z=2.33
c. z=2.58
Question 3. a. What is P(Z≤-2.53)? b. What is P(Z≥-2.53)?
Question 6. Let the random variable X denote
scores on an exam. X~N72, 64. What is the lowest
score that will be in the top 40 percent?

For a standard normal distribution, determine the probabilities
of obtaining the following z values. It is helpful to draw
a normal distribution for each case and show the corresponding
area.
(a)
greater than zero
(b)
between −2.0 and −1.5
(c)
less than 1.5
(d)
between −1.2 and 1.2
(e)
between 1.35 and 1.85

*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)

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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