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4 years ago

Please please please please please help

Mathematics

2 answers:

alex41 [277]4 years ago

4 0

Answer:

3.34

Step-by-step explanation:

german4 years ago

3 0

Answer:

2.68

Step-by-step explanation:

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The average number of words in a romance novel is 64,436 and the standard deviation is 17,071. Assume the distribution is normal

damaskus [11]

b. You're looking for the probability

Pr [72,972 ≤ X ≤ 90,043]

Transform X to Z ∼ Normal(0, 1) using the rule

X = µ + σ Z

with µ = 64,436 and σ = 17,071. Then the probability is

Pr [(72,972 - µ)/σ ≤ (X - µ)/σ ≤ (90,043 - µ)/σ]

≈ Pr [0.5000 ≤ Z ≤ 1.5000]

You probably have a z-score table available, so you can look up the probabilities to be about

Pr [Z ≤ 0.5000] ≈ 0.6915

Pr [Z ≤ 1.5000] ≈ 0.9332

and then

Pr [0.5000 ≤ Z ≤ 1.5000] ≈ 0.9332 - 0.6915 = 0.2417

c. The 75th percentile word count that separates the lower 75% of the distribution from the upper 25%. In other words, its the count x such that

Pr [X ≤ x] = 0.75

Transforming to Z and looking up the z-score for 0.75, we have

Pr [(X - µ)/σ ≤ (x - µ)/σ] ≈ Pr [Z ≤ 0.6745]

so that

(x - µ)/σ ≈ 0.6745

x ≈ µ + 0.6745σ

x ≈ 75,950

d. Because the normal distribution is symmetric, the middle 60% of novels have word counts between µ - k and µ + k, where k is a constant such that

Pr [µ - k ≤ X ≤ µ + k] = 0.6

Also due to symmetry, we have

Pr [µ - k ≤ X ≤ µ + k] = 2 Pr [µ ≤ X ≤ µ + k]

⇒ Pr [µ ≤ X ≤ µ + k] = 0.3

Transform X to Z :

Pr [(µ - µ)/σ ≤ (X - µ)/σ ≤ (µ + k - µ)/σ] = 0.3

⇒ Pr [0 ≤ Z ≤ k/σ] = 0.3

⇒ Pr [Z ≤ k/σ] - Pr [Z ≤ 0] = 0.3

⇒ Pr [Z ≤ k/σ] - 0.5 = 0.3

⇒ Pr [Z ≤ k/σ] = 0.8

Consult a z-score table:

Pr [Z ≤ k/σ] ≈ Pr [Z ≤ 0.8416]

⇒ k/σ ≈ 0.8416

⇒ k ≈ 14,367

Then the middle 60% of novels have between µ - k = 50,069 and µ + k = 78,803 words.

7 0

2 years ago

Please help with this question this is very easy!

diamong [38]

Answer:

Multiply (x)

Step-by-step explanation:

If you multiply 15.5 x 3.90 it will give you the total amount of money Chris and Jeff earned.

4 0

4 years ago

Read 2 more answers

As x increases by 1 unit, what is the exponential growth factor??

san4es73 [151]

Given:

The graph of an exponential function.

To find:

The exponential growth factor as x increases by 1 unit.

Solution:

From the given graph, it is clear that the exponential function passes through the points (1,1) and (3,9). So, the equation of the exponential must must be satisfy by these points.

The general exponential function is:

$y=ab^x$ ...(i)

Where, a is the initial value and b is the growth factor.

Putting $x=1,y=1$ in (i), we get

$1=ab^1$ ...(ii)

Putting $x=3,y=9$ in (i), we get

$9=ab^3$ ...(iii)

Divide (iii) by (ii).

$\dfrac{9}{1}=\dfrac{ab^3}{ab}$

$9=b^2$

$3=b$

b is the the growth factor and the value of b is 3.

Therefore, the exponential growth factor is 3 as x increases by 1 unit.

7 0

3 years ago

A population of rabbits is growing exponentially. The function f(x) = 5(2)t models the number of rabbits after t months.

alexandr402 [8]

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5 0

4 years ago

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Solve the equation for x<br> -x = 5 - 7x - 17

jarptica [38.1K]

Answer:

x = -2

Step-by-step explanation:

$- x = 5 - 7x - 17$

$- x = - 12 - 7x$

$- x + 7x = - 12$

$6x = - 12$

$x = - 2$

7 0

3 years ago

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