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Nady [450]
3 years ago
9

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A random sample

of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours
Mathematics
1 answer:
GuDViN [60]3 years ago
6 0

Answer: (628.48,\ 661.52)

Step-by-step explanation:

Given : Sample size : n=16 , which is a small sample (, 30) so we use t-test.

Sample mean : \overline{x}=645 \text{ hours}

Standard deviation : \sigma = 31 \text{ hours}

Significance level : \alpha=1-0.95=0.05

Critical value : t_{n-1,\alpha/2}=2.131

The confidence interval for population mean is given by :-

\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=645\pm(2.131)\dfrac{31}{\sqrt{16}}\\\\\approx645\pm16.52\\\\=(645-16.52,\ 645+16.52)\\\\=(628.48,\ 661.52)

Hence, a 95% confidence interval for the population mean \mu = (628.48,\ 661.52)

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Using a linear approximation, estimate f(2.1), given that f(2) = 5 and f'(x) = √3x-1.
algol [13]

Answer:

f\left( {2.1} \right) \approx 5.22360.

Step-by-step explanation:

The linear approximation is given by the equation

                            {f\left( x \right) \approx L\left( x \right) }={ f\left( a \right) + f^\prime\left( a \right)\left( {x - a} \right).}

Linear approximation is a good way to approximate values of f(x) as long as you stay close to the point x= a, but the farther you get from x=a, the worse your approximation.

We know that,

a=2\\f(2) = 5\\f'(x) = \sqrt{3x-1}

Next, we need to plug in the known values and calculate the value of f(2.1):

{L\left( x \right) = f\left( 2 \right) + f^\prime\left( 2 \right)\left( {x - 2} \right) }=5+\sqrt{3(2)-1}(x-2) =5+\sqrt{5}(x-2)

Then

f\left( {2.1} \right) \approx 5+\sqrt{5}(2.1-2)\approx5.22360.

6 0
3 years ago
I need the answer please
kolbaska11 [484]
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3 years ago
Which best describes the line of symmetry in the letter M
Deffense [45]

Answer:

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Step-by-step explanation:

8 0
3 years ago
For which of the following decreasing functions f does (f−1)′(10)=−1/8
Oduvanchick [21]

Recall the inverse function theorem: if f(x) has an inverse, and if f(a) = b and a = f⁻¹(b), then

f⁻¹(f(x)) = x   ⇒   (f⁻¹)'(f(x)) • f'(x) = 1   ⇒   (f⁻¹)'(f(x)) = 1/f'(x)

⇒   (f⁻¹)'(b) = 1/f'(a)

Let b = 10. Then pick the function f(x) such that f(a) = 10 and f'(a) = -8 for some number a.

7 0
2 years ago
Raleigh went to a gaming arcade for his birthday. His parents gave him $55 to spend. He purchased $14.25 in food and drinks, and
xenn [34]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Total amount to spend = $55

Amount of food and drinks purchased = $14.25

Amount put on gaming card = $(55 - 14.25) = $40.75

Cost per game = $1.25

Number of games (g) he can play

Number of games g:

Amount put on gaming card / cost per game

= $40.75 / $1.25

= 32.6 games

g ≤ 32

6 0
3 years ago
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