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andreyandreev [35.5K]
3 years ago
9

The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is

taken. What is the probability of obtaining a sample mean within 0.04 ounces of the population mean?
a. 0.9545
b. 0.0363
c. 0.3085
d. 0.5000
Mathematics
1 answer:
adelina 88 [10]3 years ago
6 0

Answer:

The standard error of the mean is 0.02

Step-by-step explanation:

Here, we want to calculate the standard error of the mean.

Mathematically;

standard error of mean = SD/ √n

where SD is the standard deviation and n is the number of samples

From the question, SD = 0.22 and n = 121

Inserting this into the equation

Standard error of the mean = 0.22/√121

= 0.22/11 = 0.02

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If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate x^4.

We have

\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h

Expand the numerator using the binomial theorem, then simplify and compute the limit.

\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}

In general, the derivative of a power function f(x) = x^n is \frac{df}{dx} = nx^{n-1}. (This is the aptly-named "power rule" for differentiation.)

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2 years ago
What is the next number on the sequence, 4, 7, 5, 8, 6, 9,___
Alchen [17]

Answer:

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Step-by-step explanation:

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joja [24]

Answer:

82°

Step-by-step explanation:

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3 years ago
X²(2 - 7x) (-x+2)<br> Expand the following exercise
Komok [63]

Answer:

Step-by-step explanation:

Use FOIL method

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x²(2-7x)(-x + 2)= x² (7x² - 16x + 4)

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