1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
victus00 [196]
3 years ago
11

A random variable x follows a normal distribution with mean d and standard deviation o=2. It is known that x is less than 5 abou

t 69.85% of the time. What is the mean d of this distribution?
Mathematics
1 answer:
Vaselesa [24]3 years ago
3 0

Answer:

The mean of this distribution is approximately 3.96.

Step-by-step explanation:

Here's how to solve this problem using a normal distribution table.

Let z be the

\displaystyle z = \frac{x - \mu}{\sigma}.

In this question, x = 5 and \sigma = 2. The equation becomes

\displaystyle z = \frac{5 - \mu}{2}.

To solve for \mu, the mean of this distribution, the only thing that needs to be found is the value of z. Since

The problem stated that P(X \le 5) = 69.85\% = 0.6985. Hence, P(Z \le z) = 0.6985.

The problem is that the normal distribution tables list only the value of P(0 \le Z \le z) for z \ge 0. To estimate  z from P(Z \le z) = 0.6985, it would be necessary to find the appropriate

Since P(Z \le z) = 0.6985 and is greater than P(Z \le 0) = 0.50, z > 0. As a result, P(Z \le z) can be written as the sum of P(Z < 0) and P(0 \le Z \le z). Besides, P(Z < 0) = P(Z \le 0) = 0.50. As a result:

\begin{aligned}&P(Z \le z)\\ &= P(Z < 0) + P(0 \le Z \le z) \\ &= 0.50 + P(0 \le Z \le z)\end{aligned}.

Therefore:

\begin{aligned}&P(0 \le Z \le z) \\ &= P(Z \le z) - 0.50 \\&= 0.6985 - 0.50 \\&=0.1985 \end{aligned}.

Lookup 0.1985 on a normal distribution table. The corresponding z-score is 0.52. (In other words, P(0 \le Z \le 0.52) = 0.1985.)

Given that

  • z = 0.52,
  • x =5, and
  • \sigma = 2,

Solve the equation \displaystyle z = \frac{x - \mu}{\sigma} for the mean, \mu:

\displaystyle 0.52 = \frac{5 - \mu}{2}.

\mu = 5 - 2 \times 0.52 = 3.96.

You might be interested in
What is the distance from the origin to point A graphed on the complex plane below?
Lisa [10]

Answer:

a. square root of 5

b. square root of 13

c. 9

d. 13

Step-by-step explanation:

6 0
3 years ago
Whats the product of 6 and<br><br> q
nevsk [136]

Answer:

6q or 6 * q

Step-by-step explanation:

As you do not know what the value of the variable q is, you are essentially changing it from word form to expression form.

"product" in math means multiply, so you are multiplying 6 with q.

6q is your answer.

~

7 0
3 years ago
Read 2 more answers
Solve the system.
svetoff [14.1K]

Answer:

(0, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y + 5x = 1

5y - x = 5

<u>Step 2: Rewrite Systems</u>

y + 5x = 1

  1. Subtract 5x on both sides:                    y = 1 - 5x

<u>Step 3: Redefine Systems</u>

y = 1 - 5x

5y - x = 5

<u>Step 4: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitution in <em>y</em>:                      5(1 - 5x) - x = 5
  2. Distribute 5:                             5 - 25x - x = 5
  3. Combine like terms:                5 - 26x = 5
  4. Isolate <em>x</em> term:                          -26x = 0
  5. Isolate <em>x</em>:                                   x = 0

<u>Step 5: Solve for </u><em><u>y</u></em>

  1. Define equation:                    5y - x = 5
  2. Substitute in <em>x</em>:                       5y - 0 = 5
  3. Subtract:                                 5y = 5
  4. Isolate <em>y</em>:                                 y = 1
8 0
2 years ago
In a 10 m2 ecosystem, there are 20 raccoons. The population density of raccoons is _____.
katrin2010 [14]
To find the density of racon all you have to do is to divide number of racoons with surface area because as name says you need to get x number of racoons per m^2

its own name tells you what you need to divide with what.

answer is:
20/10 = 2 raccoons per m^2
8 0
3 years ago
Read 2 more answers
5 (i + 2) = 8 (i -1)
Vinil7 [7]
5(i + 2) = 8(i -1)
5i + 10 = 8i -8
-3i + 10 = -8
-3i = -18
i = 6
5 0
3 years ago
Other questions:
  • Gerry had a coupon for $0.25 off a
    10·2 answers
  • What is the value of r in the equation 4r − 8 = 5r + 12?
    14·2 answers
  • Can y’all help please . i don’t know how to do this .
    13·2 answers
  • Need help ASAP thanks!
    7·1 answer
  • Suppose 42% of the population has myopia. If a random sample of size 442 is selected, what is the probability that the proportio
    5·1 answer
  • Please help these are the last ones I need I will mark you as brainliest if you answer them correctly! Ty
    12·1 answer
  • Help me find the volume of this shape. step-by-step explanation please!!
    13·1 answer
  • Brainliest,<br><br>s/-9 =9 <br>what does s represent?​
    9·2 answers
  • Find p(-3) if p(x)= 4x^3 - 5x^2 + 7x - 10.
    8·1 answer
  • Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!