A company's sales force makes 400 sales calls, with + 0.25 probability that a sale will be made on a call. What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made? Enter your answer as a decimal value, rounded to 4 decimal places.

Answers

Answer 1

Answer:

0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.

Step-by-step explanation:

We use the normal approximation to the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call.

This means that [tex]n = 400, p = 0.25[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 400*0.25 = 100[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.25*0.75} = \sqrt{75}[/tex]

What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made?

Using continuity correction, this is [tex]P(55+0.5 \leq X \leq 75-0.5) = P(55.5 \leq X \leq 74.5)[/tex], which is the p-value of Z when X = 74.5 subtracted by the p-value of Z when X = 55.5.

X = 74.5

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

[tex]Z = \frac{74.5 - 100}{\sqrt{25}}[/tex]

[tex]Z = -2.94[/tex]

[tex]Z = -2.94[/tex] has a p-value of 0.0016

X = 55.5

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

[tex]Z = \frac{55.5 - 100}{\sqrt{25}}[/tex]

[tex]Z = -5.14[/tex]

[tex]Z = -5.14[/tex] has a p-value of 0

0.0016 - 0 = 0.0016

0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.


Related Questions

The y value is two less than twice the x-value

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Candice .... who’s Candice...alll .for nothing at all

What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)

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Answer:

i honestly dk but need help

Step-by-step explanation:

ls

Answer:

2m+2n+7

Step-by-step explanation:

See image below:)

3p(2p - 9) - 2p(-9 + p)​

Answers

Answer:

4p² - 9p

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

3p(2p - 9) - 2p(-9 + p)

Step 2: Simplify

[Distributive Property] Distribute 3p:                                                               6p² - 27p - 2p(-9 + p)[Distributive Property] Distribute -2p:                                                             6p² - 27p + 18p - 2p²[Subtraction] Combine like terms (p²):                                                            4p² - 27p + 18p[Addition] Combine like terms (p):                                                                   4p² - 9p
3p(2p-9)-2p(-9+p)
6p -27p -2p^2+12p
4p^2 -27p+18p
Combine like terms
Your answer is 4p^2 -9p

what is 12 take away 1 3/5​

Answers

10 3/5

thank your guy for the pool work

Find the value of the expression (4x – 12)+(1/3xy – 5) when x = 6 and y=2

Answers

Answer:

11

Step-by-step explanation:

GIVEN

x = 6

y = 2

STEPS

(4x - 12) + (1/3xy - 5 )

(4(6) - 12 ) + ( 1/3(6x2) - 5)

(24 - 12) + ( 1/3(12) - 5)

12 + (4 - 5)

12 + (-1)

(12 - 1)

11

Write a statement that indicates that the triangles in each pair are congruent. NO LINKS!!​

Answers

Answer:

23

UVW congruent to WFG

and

24

FHG congruent to LMN

Answer:

23 ) UVW is congruent to WGF

24 ) FHG is congruent to LMN

John made a small rectangular table for his workroom. If the sides of the table are 32 inches and 26 inches, what should the table measure diagonally?

Answers

Answer:

The table should measure diagonally about 41.23 inches.

Step-by-step explanation:

To find the diagonal of a rectangle we use the formula :

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

A and B both represent the side lengths of the rectangle, while C is the diagonal part. Knowing this formula, let's plug in the values for A and B and see what happens.

[tex]32^{2}[/tex] + [tex]26^{2}[/tex] = [tex]c^{2}[/tex]

1024 + 676 = [tex]c^{2}[/tex]

1700 = [tex]c^{2}[/tex]

The square root of 1700 is (rounded to the hundreth's place) = 41.23

Answer:

c41

Step-by-step explanation:

10) Using Limit Comparison Test (LCT), the following series
+00
M:
-1 + 2n5
n6 + 1
n=1​

Answers

Compare to the divergent series,

[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]

Then by the limit comparison test, the given series also diverges, since the limit

[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{2n^5-1}{n^6+1}}{\frac1n} = \lim_{n\to\infty}\frac{2n^6-n}{n^6+1}=\lim_{n\to\infty}\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2[/tex]

is positive and finite.

Which summation properties or formulas must be used to evaluate this summation? Check all that
apply

Answers

Given:

Summation problem is:

[tex]\sum\limits_{n=1}^{35}n(n^2+1)[/tex]

To find:

The properties or formulas must be used to evaluate the given summation.

Solution:

We have,

[tex]\sum\limits_{n=1}^{35}n(n^2+1)[/tex]

In can be rewritten as:

[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\sum\limits_{n=1}^{35}(n^3+n)[/tex]

[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\sum\limits_{n=1}^{35}n^3+\sum\limits_{n=1}^{35}n[/tex]        [tex]\left[\because \sum\limits_{i=1}^n(a_i\pm b_i)=\sum\limits_{i=1}^na_i\pm \sum\limits_{i=1}^nb_i\right][/tex]

[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\left[\dfrac{35(35+1)}{2}\right]^2+\dfrac{35(35+1)}{2}[/tex]  [tex]\left[\because \sum\limits_{i=1}^ni=\dfrac{n(n+1)}{2},\sum\limits_{i=1}^ni^3=\left[\dfrac{n(n+1)}{2}\right]^2\right][/tex]

[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\left[\dfrac{35(36)}{2}\right]^2+\dfrac{35(36)}{2}[/tex]

[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\left[630\right]^2+630[/tex]

[tex]\sum\limits_{n=1}^{35}n(n^2+1)=396900+630[/tex]

[tex]\sum\limits_{n=1}^{35}n(n^2+1)=397530[/tex]

Therefore, the properties and formula used are:

[tex]\sum\limits_{i=1}^n(a_i\pm b_i)=\sum\limits_{i=1}^na_i\pm \sum\limits_{i=1}^nb_i,\\\sum\limits_{i=1}^ni=\dfrac{n(n+1)}{2},\\\sum\limits_{i=1}^ni^3=\left[\dfrac{n(n+1)}{2}\right]^2[/tex]

Answer: see attachment below

Step-by-step explanation:

if the given ordered pair equal then find value of x and y
(3x+5)=(x+2)
and (4y+7)= (y+3)

Answers

Answer:

3x+5 =x+2

3x-x=2-5

2x= –3

x=-3/2

4y+7=y+3

4y–y =3-7

3y=–4

y= —4/3

Use the Pythagorean theorem to find the value for ( show work )

Answers

Answer:

x = 12

Step-by-step explanation:

x^2 + (x - 7)^2 = (x + 1)^2

x^2 + x^2 - 14x + 49 = x^2 + 2x + 1

x^2 - 16x + 48 = 0

(x - 4)(x - 12) = 0

x - 4 = 0 or x - 12 = 0

x = 4 or x = 12

One side has length x - 7.

For x = 4, x - 7 = 4 - 7 = -3.

Since a side of a triangle cannot have a negative length, x = 4 must be discarded.

Answer: x = 12

Delia bought 32 fluid ounces of fruit juice. How many gallons of juice did she buy?


A. 1
B. 0.5
C. 0.25
D. 0.2

Answers

Answer:

the answer is C. 0.25.

Step-by-step explanation:

simply converting the fluid oz into gallons.

The answer is c. 0.25

Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 15 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Kyle, Carol, and Adam are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.

Answers

Answer:

1 / 1365

Step-by-step explanation:

Given that :

Number of employees to choose from = 15

Number of employees to be chosen = 4

Probability of choosing You, Kyle, Carol and Adam

Recall ;

P(A) = number of required outcome / Total possible outcomes

Number of required outcome = 4C4

Total possible outcomes = 15C4

nCr = n! ÷ (n-r)!r!

Using calculator to save computation time :

15C4 = 1365

4C4 = 1

P(choosing you, Kyle, Carol and Adam) :

1 / 1365

What is the measure of angle AIN?
O
A. 95°
B. 125°
C. 55
o
O
D. 30°

Answers

Answer:

30

Step-by-step explanation:

AIN is a vertical angle to FIL, which means they ae equal

FIL = 30 so AIN = 30

PLS HELP!! I NEED TO FIND THE SURFACE AREA OF THIS CYLINDER!!!!!

Answers

Answer:

Step-by-step explanation:

you have two disks, and one rectangle

area of the disk = π [tex]r^{2}[/tex]

47 π x 2 = 94 π (for the two disks....

rectangle area = L x W

width = 14

Length = 2*π*r = 14π

area = 14*14π = 196 π

total = 196 π + 94 π = 290 π

Answer:

The surface area of this cylinder is about 923.63 [tex]inches^{2}[/tex].

Step-by-step explanation:

The formula for the surface area of a cylinder is this :

[tex]A = 2\pi rh+2\pi r^{2}[/tex]

"R" is 7, and "h" is 14. Knowing these values, let's solve.

[tex]A = 2\pi rh+2\pi r^{2}[/tex] = 2 · π · 7 · 14 + 2 · π ·72 ≈ 923.62824

The surface area of this cylinder is about 923.63 [tex]inches^{2}[/tex].

Hope this helps, please mark brainliest! :)

HELP! Please!

Create an equation to model a population of cells which starts with 10 cells and doubles in size every day. How many days will it take to reach 1,000,000 cells?

Answers

Answer:

it will take 100,000 more days.

you can do this by dividing 10 and 1,000,000

7) Point P is located at (4,8) on a coordinate plane. Point P will be relfected over y = x. What will bee
the coordiantes of the image of point P?
A. (28,4)
B. 24,8)
C. (4,28)
D. (8,4)

Answers

I think the answer is A 28,4 I hopes this helps

Which completely describes the polygon ? equilateral equiangular regular congruent

Answers

Answer: C) regular

Explanation:

Any regular polygon is both equilateral and equiangular.

Equilateral = all sides are equal

Equiangular = all angles are equal

A local dealership provides you with statistics that show the number of each color car they sold last year along with the percentages that those sales represented relative to their inventory for that color car.

For each color, how many cars did the dealership have in its inventory before they started selling them?

Answers

Answer:

red: 20

white: 30

black: 25

silver: 40

other: 12

Step-by-step explanation:

To find the original number of cars per color in the inventory, divide the sold number of cars by the percent of the inventory.

red: 20 = 10/0.5

white: 30 = 21/0.7

black: 25 = 19/0.76

silver: 40 = 10/0.25

other: 12 = 4/0.33

Find the difference,
(20m+ 3) - (7m - 5)
A. 27m - 2
B. 13m +8
C. 27m +8
D. 13m - 2
SUBMU

Answers

Answer:

B 13m+8

Step-by-step explanation:

(20m+3) - (7m-5)

20m+3-7m+5

13m+8

The answer is B. 13m+8

Find the surface area of the prism. 13 in. 3 in 7 in.​

Answers

Answer:

182+78+42=302 ... 302's ya answer...Give me brainiest answer to say ty! :)

Step-by-step explanation:

I just need to know what is m=

Answers

Answer:

- 2

Step-by-step explanation:

Given :

Point A = (-1, 4)

Point B = (1, 0)

x2 = - 1 ; y2 = 4 ; x1 = 1 ; y1 = 0

Rise = (y2 - y1) = 4 - 0 = 4

Run = (x2 - x1). = - 1 - 1 = - 2

Slope = Rise / Run = 4 / - 2 = - 2

The slope, m = - 2

The average height of corn stalks in a field is 71 inches with a standard deviation of 4.3 inches. Sketch a normal curve labeling the horizontal axis at one, two, and three standard deviations from the mean.

Answers

Answer:

The answer is below

Step-by-step explanation:

The empirical rules states that for a normal distribution, 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within three standard deviations from the mean.

Given that:

mean (μ) = 71 inches, standard deviation (σ) = 4.3 inches

One standard deviation = μ ± σ = 71 ± 4.3 = (66.7, 75.3)

Two standard deviation = μ ± 2σ = 71 ± 2*4.3 = (62.4, 79.6)

Three standard deviation = μ ± 3σ = 71 ± 3*4.3 = (58.1, 83.9)

The graph is attached

what is 5a +14=3(a +2)​

Answers

Answer:

a=-4

Step-by-step explanation:

See image below:)

This is my workings


Please help please and thanks

Answers

This will help a lot if you go to desmos! Just graph the equation on there! It’s much easier to see on computer

The stock of Company A gained 6% today to $87.45. What was the opening price of the stock in the beginning of the day?

25 POINTS!!!!!!!!!!!!!!!!

Answers

Answer:

$82.50

Step-by-step explanation:

gainsd 6%=106%

$87.45×100%/106%=$82.50

Hope can help!!!

Answer:

$82.50

Step-by-step explanation:

gained6%=100%+6%

100%+6%=$87.45

100%=?

solution :

$87.45×100/106=$82.50

what are the prime factors of the greatest 4 digit number?​

Answers

Answer:

The prime factors of the greatest 4 digit number are 3, 11 and 101.

Step-by-step explanation:

Hope it helps

The prime factors of greates 4 digit is 3,11 101

Which rule explains why these triangles are congruent?

Answers

SSS
hope this helps!!

HELP DUE SOON 20 POINTS

Answers

Answer:

x = 10

Step-by-step explanation:

m∠KNL = 90

10x - 10 = 90

10x = 100

x = 10

What are the coordinates of the point plotted on this graph?

Answers

Answer:

C

Step-by-step explanation:

Correct answer

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