Mathematics, 26.06.2020 16:01 ineedhelp2285

Z=1.23 z=0.86 WHAT is the area of the shaded region between the two

Answers: 2

Show answers

Answers

Answer from: jakeagilbert

The area of the shaded region between $\\ z = 1.23$ and $\\ z = 0.86$ is $\\ P(0.86 < z < 1.23) = 0.08554$ or 8.554%.

Step-by-step explanation:

To solve this question, we need to find the corresponding probabilities for the standardized values (or z-scores) z = 1.23 and z = 0.86, and then subtract both to obtain the area of the shaded region between these two z-scores.

We need to having into account that a z-score is given by the following formula:

$\\ z = \frac{x - \mu}{\sigma}$

Where

x is a raw score from the distribution that we want to standardize using [1]. $\\ \mu$ is the mean of the normal distribution. $\\ \sigma$ is the standard deviation of the normal distribution.

A z-score indicates the distance of x from the mean in standard deviations units, where a positive value "tell us" that x is above $\\ \mu$ , and conversely, a negative that x is below $\\ \mu$ .

The standard normal distribution is a normal distribution with $\\ \mu = 0$ and $\\ \sigma = 1$ , and has probabilities for standardized values obtained using [1]. All these probabilities are tabulated in the standard normal table (available in any Statistical book or on the Internet).

Using the cumulative standard normal table, for $\\ z = 1.23$ , the corresponding cumulative probability is:

$\\ P(z$

The steps are as follows:

Consult the cumulative standard table using z = 1.2 as an entry. Z-scores are in the first column of the mentioned table. In the first row of it we have +0.00, +0.01, +0.02 and, finally, +0.03. The probability is the point that result from the intersection of z = 1.2 and +0.03 in the table, which is $\\ P(z$ .

Following the same procedure, the cumulative probability for $\\ z = 0.86$ is:

$\\ P(z$

Subtracting both probabilities (because we need to know the area between these two values) we finally obtain the corresponding area between them (two z-scores):

$\\ P(0.86 < z < 1.23) = 0.89065 - 0.80511$

$\\ P(0.86 < z < 1.23) = 0.08554$

Therefore, the area of the shaded region between $\\ z = 1.23$ and $\\ z = 0.86$ is $\\ P(0.86 < z < 1.23) = 0.08554$ or 8.554%.

We can see this resulting area (red shaded area) in the graph below for a standard normal distribution, $\\ N(0, 1)$ , and $\\ z = 0.86$ and $\\ z = 1.23$ .

Z=1.23 z=0.86 WHAT is the area of the shaded region between the two

Answer from: Quest

The answer is $9.90 with rounding to the nearest tenth

Answer from: Quest

42.4

step-by-step explanation:

convert to decimal

Another question on Mathematics

Mathematics, 21.06.2019 13:40

Use the distance formula to determine the distance that point q is from r on the hypotenusebased on a 2-3 ratio.i need asap !

Answers: 3

Answer

Mathematics, 21.06.2019 18:00

For a field trip to the zoo, 4 students rode in cars and the rest filled nine busess. how many students were in each bus if 472 students were on the trip

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

What is the name of a polygon that has four congruent sides and theses angle measures 60,120,60,120?

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

Awoman has 14 different shirts: 10 white shirts and 4 red shirts. if she randomly chooses 2 shirts to take with her on vacation, then what is the probability that she will choose two white shirts? show your answer in fraction and percent, round to the nearest whole percent.

Answers: 1

Answer

You know the right answer?

Z=1.23 z=0.86 WHAT is the area of the shaded region between the two...

Questions