Question

Find the percentage of the area under a normal curve between the mean and the given number of standard deviations from the mean. - 0.43

Can you explain how to get the z-score?

Answer #1

We already know from symmetry

*P* ( *Z*<0 )=0.5.

We see that *P* ( *Z*<0.43 )=0.6664 from table
shown below

*P* ( *Z*<?0.43)=1?*P* (
*Z*<0.43 )=1?0.6664=0.3336

hence

*P* (?0.43<*Z*<0 )=0.5- 0.3336 =
**0.1664 = 16.64%**

Find the percent of area under a normal curve between the mean
and the given number of standard deviations from the mean. (Note
that positive indicates above the mean, while negative indicates
below the mean.) 0.80 ____% (Round to the nearest tenth as
needed.)

In Exercises 16 and 17, find the indicated area under the curve
of the standard normal distribution, then convert it to a
percentage and fill in the blank.
16. About _______% of the area is between z = -0.75 and z = 0.75
(or within 0.75 standard deviations of the mean).
17. About _______% of the area is between z = -1.5 and z = 1.5
(or within 1.5 standard deviations of the mean).

The values of z-score are given.
1a.) Find the area under the normal curve to the right of
z = -0.86. Round the answer to four decimal places.
The area under the normal curve to the right of z =
-0.86 is ____.
1c.) Find the area under the normal curve between z =
-0.32 and z = 0.92. Round the answer to four decimal
places.
The area under the normal curve between z = -0.32 and
z = 0.92...

1. About ____ % of the area under the curve of the standard
normal distribution is between z = − 1.863 z = - 1.863 and z =
1.863 z = 1.863 (or within 1.863 standard deviations of the
mean).
2. About ____ % of the area under the curve of the standard
normal distribution is outside the interval
z=[−2.24,2.24]z=[-2.24,2.24] (or beyond 2.24 standard deviations of
the mean).
3. About ____ % of the area under the curve of the...

Find the indicated area under the curve of the standard normal
distribution; then convert it to a percentage and fill in the
blank.
About ______% of the area is between
zequals=minus−3.5
and
zequals=3.5
(or within 3.5 standard deviations of the mean).
About
nothing%
of the area is between
zequals=minus−3.5
and
zequals=3.5
(or within 3.5 standard deviations of the mean).

1. Find the area under the standard normal curve to the left of
z = 1.66.
2. Find the area under the standard normal curve between z =
-1.75 and z = 0.96.
3. Find the z-score for which the area to its right is 0.67.
4. A normal population has mean 176=m and a standard deviation
.38=s What proportion of the population is more than 185?

Sketch the area under the standard normal curve over the
indicated interval and find the specified area. (Round your answer
to four decimal places.) The area between z = −2.15 and z = 1.34 is
.
Sketch the area under the standard normal curve over the
indicated interval and find the specified area. (Round your answer
to four decimal places.) The area between z = −1.33 and z = 2.03 is
.
Sketch the area under the standard normal curve...

Find the area under the standard normal curve that lies between
the following two z values. Round your answers to at least four
decimal places.
(a)Find the area under the standard normal curve that lies
between = z − 1.28 and = z 1.36 .
(b)Find the area under the standard normal curve that lies
between = z − 2.17 and = z − 1.92 .
(c)Find the area under the standard normal curve that lies
between = z 1.36...

1.
One hundred percent of scores fall under the area of the normal
curve.
true
false
2. A z score tells nothing about the distance of a score from
the mean.
true
false
3. A z score does NOT allow for the comparison of different
scores from different distributions
true
false
4. A number whose z score is equal to zero is equal to the
mean.
true
false
5. Which of the following is not a characteristic of the
normal...

2. a) Find the area under the standard normal curve to the right
of z = 1.5.
b) Find the area under the standard normal curve to the left of
z = 1.
c) Find the area under the standard normal curve to the left of
z = -1.25.
d) Find the area under the standard normal curve between z = -1
and z = 2.
e) Find the area under the standard normal curve between z =
-1.5 and...

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