In a certain normal distribution, find the mean μ when σ = 5 and 5.48% of the area lies to the left of 78.

Answers

Answer 1

The mean of the normal distribution, using the formula for the z-score, considering the given data, is of 86.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The standard deviation is of [tex]\sigma = 5[/tex].5.48% of the area lies to the left of 78, hence when X = 78, Z has a p-value of 0.0548, that is, Z = -1.6.

Then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.6 = \frac{78 - \mu}{5}[/tex]

[tex]78 - \mu = -1.6(5)[/tex]

[tex]\mu = 86[/tex]

More can be learned about the normal distribution at https://brainly.com/question/24663213


Related Questions

help me fast pleas-

help meeeeeeeeeeeeee

Answers

Hidden Treasures Walking Tour:
y= 9 x 6 + 25
= 79

Road-Less-Traveled Tours:
the function is y= 12x
y= 12 x 6 = 72

Bowman Bros:
The line is y -30 over x -1 = 50 - 30 over 3 - 1
y= 10x + 20

y= 10 x 6 + 20 = 80

72 < 79 < 80
So chose Road-Less-Travelled Tours

What is the first step you would take to solve the equation 1 1/2 + 2 1/3 = ?

A. First, you should convert the mixed numbers to improper fractions.

B. First, you should simplify the fractions with the GCF.

C. First, you should clearly state your final answer.

D. First, you should multiply the numerators and denominators.

Answers

The first step to solve the equation 1 1/2 + 2 1/3 = ? is (a) First, you should convert the mixed numbers to improper fractions.

How to determine the first step?

The equation is given as:

1 1/2 + 2 1/3 = ?

The terms in the equation are mixed numbers.

So, the first stem is to convert the mixed numbers to improper fractions

Hence, the true statement is (a) First, you should convert the mixed numbers to improper fractions.

Read more about fractions at:

https://brainly.com/question/1622425

Eric jog 3 1\4 miles on Monday 5 5\8 miles on Tuesday and 8 miles on Wednesday suppose he continues the pattern for the remainder of the week how far will Eric jog on Friday

Answers

Step-by-step explanation:

first, let's bring everything to the same fraction denominator, which would be 1/8 to cover all.

so, he jogs

3 2/8 miles on Monday

5 5/8 miles on Tuesday

8 0/8 miles on Wednesday

the difference from day to day is

5 5/8 - 3 2/8 = 2 3/8 (subtract the whole numbers and then also the fractional part).

to control :

5 5/8 + 2 3/8 = 7 8/8 = 8

so, he adds every day 2 3/8 miles.

that means in 2 days (from Wednesday to Friday) this will be additional 2×(2 3/8) = 4 6/8 = 4 3/4 miles.

so, he will jog

8 + 4 3/4 = 12 3/4 miles

on Friday.

don't forget, when we write something like 2 3/8. we actuality mean (2 + 3/8). and all rules about handling, transforming and calculating expressions apply.

therefore, e.g

2×(2 3/8) = 2×(2 + 3/8) = 4 + 6/8 = 4 6/8 = 4 3/4

WILL GIVE BRAINLIEST. Explain how you would prove that this is an identity. (Please explain in understandable terms)

Answers

Answer:

Step-by-step explanation:

I would first expand out the numerator since it would become [tex]\sin^{2} x+2\sin x \cos x+\cos^{2}x[/tex], which would allow me to use the double angle formula for sine and the Pythagorean identity.

Which of the following is not a linear function?

Answers

Answer:

Step-by-step explanation:

Answer:

A is not linear.

Step-by-step explanation:

This is my proof when I put it on my graphing calculator.

condense each expression [tex]5log {_{5} } x-\frac{1}{4} log_{5} (8-x)[/tex]

Answers

Answer:

5 log₅ x − ¼ log₅ (8−x)

log₅ x⁵ − log₅ (8−x)^¼

log₅ x⁵ − log₅ ∜(8−x)

log₅ (x⁵ / ∜(8−x))       is the answer

Step-by-step explanation:

hope this helps

Answer:

[tex]log_5\biggr(\frac{x^5}{(8-x)^{\frac{1}{4}}}\biggr)[/tex]

Step-by-step explanation:

[tex]5log_5(x)-\frac{1}{4}log_5(8-x)\\ \\log_5(x^5)-log_5((8-x)^{\frac{1}{4}})\\\\log_5\biggr(\frac{x^5}{(8-x)^{\frac{1}{4}}}\biggr)[/tex]

man helppppp oooooooooo

Answers

your answer is right since your going to the right +3 and decreasing -9 units

Pomegranate, Papaya, and Lychee

Answers

Answer:

they're fruits

Step-by-step explanation:

i dont really know what the question is... they help against heart disease, cancer and diabetes

hi! what’s the square root of 82 rounded to the nearest tenth?

Answers

Answer:

9.1

Step-by-step explanation:

I went into my calculator and typed in [tex]\sqrt{82}[/tex] and I was given:

9.055385...

So to round the nearest tenth, you look at the tenths place (which is 0) and go one number behind that (which is 5). Since the number behind the tenths place is 5 or higher, you round up to 1

-2(3x-5)=4(x+3)+8

Please will give brainlyest

Answers

Answer:

x=-1

Step-by-step explanation:

-2(3x-5)=4(x+3)+8

-6x+10=4(x+3)+8

-6x+10=4x+12+8

-6x+10=4x+20

-6x+10-10=4x+20-10

-6x=4x+10

-6x-4x+10-4x

-10x=10

[tex]\frac{-10}{-10}= \frac{10}{-10}[/tex]

x=-1

Find the Volume of a cylinder with a diameter of 5 in and the height of 10 in. Use π = 3.14

Answers

Answer:

196.25in^3

Step-by-step explanation:

[tex]diameter(d) = 5in \\ radius(r) = 2.5in \\ height(h) = 10in \\ \\ volume = \pi {r}^{2} h \\ volume = 3.14 \times {2.5in}^{2} \times 10in \\ volume = 196.25 {in}^{3} [/tex]

Shannon is building a rectangular garden that is 18 feet wide and 27 feet long. Write an equation that represents the area of Shannon’s garden. In your equation, let g represent the area of Shannon’s garden. Then solve your equation

Answers

g=18x27 g=486sq feet

The slope of a line is given by the formula:
horizontal change
m
vertical change
True
False

Answers

Answer:

The answer is True

Express as a trinomial.
(3-10) (2x + 2)

Answers

The answer is -14x-14

Compare the numbers 289.4 and 289.400 using >,<, or =

Answers

Answer:

289.4 = 289.400

Step-by-step explanation:

no matter how many 0s are added to the end theyre always gonna be the same

Solve this Question and Write the method how to find LCM.​

Answers

Answer:

8a²b

Step-by-step explanation:

Least common multiple:  The smallest number that is a multiple of two or more numbers

As  2a² has a²  and 8ab has b, then the least common multiple will include a²b.

8 is a multiple of 2

Therefore, the LCM is 8a²b

What is a dividend if the question is 1/2 divided by 1/4 =

Answers

Answer:

2

Step-by-step explanation:

Multiply the numerator of 1/2 with the denominator of 1/4 to get 4. Then multiply the denominator of 1/2 with the numerator of 1/4 to get 2. Lastly divide 4 by 2 to get 2.

Select all the expressions that are equivalent to 9 + 7x – 3y.

Answers

Answer:

4 or 9+7x+(-3y) is the only expression equivalent

Step-by-step explanation:

Number 4 is the only expression that comes out to be equivalent because the rest of the answer choices have something wrong with them.

Step-by-step explanation:

Find the value of x

A. 25°
B. 85°
C. 75°
D. 105°

Answers

Answer:

C

Step-by-step explanation:

I took the test and got it right

Answer:

C: 75 degrees

Step-by-step explanation:

180-155=25 which makes the angle to the other side of angle x

80+25=105

180(full angle measurement of triangle)-105=75

Btw I also had this on my quiz and got it right

Tim bought a certain number of bags of chips that each cost $1.05. Find the cost of 2 bags.

Answers

Answer:

$2.10

Step-by-step explanation:

To get this answer all you have to do is, $1.05 x 2 = $2.10

the answer will be 2:10

The price of Stock A at 9 A.M. was ​$12.41. Since​ then, the price has been increasing at the rate of ​$0.12 each hour. At noon the price of Stock B was ​$13.16. It begins to decrease at the rate of ​$0.14 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answers

Answer:

1.50 Hours

Step-by-step explanation:

Given:

→ The price of Stock A at 9 A.M. was ​$12.41. → Since​ then, the price has been increasing at the rate of ​$0.12 each hour. → At noon the price of Stock B was ​$13.16. → It begins to decrease at the rate of ​$0.14 each hour.

To Find:

If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Solve:

Price of stock A at 9 a.m.= $12.41

The price has been increasing at the rate of ​$0.12 each hour.

Increase in price after 3 hours = 0.12 × 3 = 0.36

Price of Stock A at noon= 12.41+0.36 =12.77

Let n be the no. of hours after which the prices of both the stocks will be same .

So, Increase in price after n hours = 0.12 n

Price of Stock A after n hours = 12.77+0.12 n

Price of stock B = 13.16

The price has been decreasing at the rate of ​$0.14 each hour.

Let n be the no. of hours

So, Increase in price after n hours = 0.14 n

Price of Stock B after n hours =13.16-0.14 n

ATQ

12.77 + 0.12n = 13.16 - 0.14n

-12.77 + 13.16 = 0.12n + 0.14n

0.39 = 0.26n

0.39/0.26 = n

n = 1.50

Hence the prices of the two stocks be the​ same after 1.50 hours after 12 pm .

~Learn with Lenvy~

What is the equation of the line that passes through the point ( 2 , − 3 ) (2,−3) and has a slope of 2

Answers

Answer: y = 2x -7

Step-by-step explanation:

The equation of a line is in the form y = mx + b

We know m = 2

So, y = 2x + b

we need to find b, and we can use either point given to find it:

lets use (2, -3):

-3 = 2(2) + b

-7 = b

now we know, the line's equation is y = 2x -7

If we drop a rock near the surface of Earth, its velocity increases by 32 feet per second for each second the rock falls. Is the velocity of the rock a linear function of the time since it was dropped?

Answers

The velocity of the rock is the number of feet traveled per second

The velocity of the rock is a linear function of time

How to determine the function?

From the question, we understand that the velocity increases by 32 feet per second for each second

This means that we have the following rates:

Velocity = 0, 32, 64, 96, 128....

Notice that the difference between adjacent numbers is 32.

This means that the velocity changes at a constant rate or slope

Hence, the velocity of the rock is a linear function

Read more about linear functions at:

https://brainly.com/question/15602982

what is 36 more than 40



Answers

Answer:

76.

Step-by-step explanation:

Forty "more" implies that you are adding forty to thirty-six. Making it seventy-six.

The number that is 36 more than 40 will be 76.

What is Algebra?

Algebra is the analysis of abstract symbols, while reasoning is the manipulation of all those views.

The definition of unsophistication is making something simpler to achieve or grasp while also making it a little less difficult.

Let 'x' be the number that is 36 more than 40. Then the equation is given as,

x = 36 + 40

Add the number 36 and 40, then we have

x = 36 + 40

x = 76

The number that is 36 more than 40 will be 76.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

What’s the answer to this question

Answers

Answer:

398 * 1.034^t

Step-by-step explanation:

P = 398(1 + 3.4%)^t = 398 * 1.034^t

20 points! I appreciate it! What is the difference in the areas of the two triangles?

Answers

Answer:

1 ft²

Step-by-step explanation:

Left triangle, area = 10 x 7/2 = 35 ft²

Right triangle, area = 9 x 8/2 = 36 ft²

Difference = 1 ft²

Which of the following is the graph of an odd-degree polynomial with a positive lead
coefficient?

(Answer choices are in the image)

Answers

The answer selected should already be the right answer.

An even number of total minimum/maximums indicates an odd-degree polynomial. For example, only the 3rd and 4th graphs are odd-degree because they have four mins/maxes total.

For the polynomial to have a positive leading coefficient, the line must go up in the positive direction. For example, only the 1st and 3rd graphs have a positive leading coefficient because their right-most line is going upwards.

The 3rd graph is the only answer choice with both of these characteristics, making it the right answer.

The third graph is the only one that is an an odd-degree polynomial with a positive lead coefficient.

How to Interpret the graph of a Polynomial?

An even number of total minimums/maximums of the Polynomial is classified as an odd-degree polynomial. Now, we see that only the 3rd and 4th graphs are odd-degree polynomials because they have four total minimums/maximums.

For the polynomial to have a positive leading coefficient, the line must go up in the positive direction. This means that only the 1st and 3rd graphs have a positive leading coefficient due to the fact that their right-most line is going upwards.

Thus, we can say that the third graph is the only one that is an an odd-degree polynomial with a positive lead coefficient.

Read more about Polynomial Graph at; https://brainly.com/question/4685884

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How many 1/3 cup servings are in 9 cups of homemade soup

Answers

Answer:

27

Step-by-step explanation:

9 divided by 1/3 is 9 times 3 which is 27

On a jogging trail, you take a random sample of the speed of 50 joggers and determine that their average speed is 5.3 mph. Which statement is true?

A) You conclude that the average speed of all joggers is close to 5.3 mph.
B) You conclude that the speed of all joggers on this trail is exactly 5.3 mph.
C) You conclude that the average speed of all joggers on this trail is close to 5.3 mph.
D) You conclude that the speed of more than half of the joggers on this trail is less than 5.3 mph.

Answers

C.) You conclude that the average speed of all joggers on this trail is close to 5.3mph

Please show work and thank you

Answers

Step-by-step explanation:

since it's an isosceles triangle, DE = EF

i.e. 8x-13 = 5x+ 17

or 8x -5x = 17 +13

or 2x = 30

or X = 15

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