Mathematics, 02.10.2019 00:00 Pookiev

2. you have tested bearings for a particular machine. this resulted in a mean of 30,457,500 cycles with a standard deviation of 167,800 cycles (assume approximately normally distributed). (a.) what percentage of the bearings will last for 30,000,000 cycles? (b.) if the manufacturer is willing to accept a 5% failure rate, what warranty time should he put on the bearings?

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Answer from: queenkimm26

(a) 99.68% of the bearings will last for 30,000,000 cycles

(b) The manufacturer should put 30,181,494 cycles of warranty time on the bearings

Step-by-step explanation:

Let X be the random variable that represents the cycles of the bearings. We know that X is approximately normally distributed with a mean of $\mu$ = 30, 457, 500 cycles and a standard deviation of $\sigma$ = 167, 800 cycles. Then, we can assume that the normal probability density function for X is given by

$f(x) = \frac{1}{\sqrt{2\pi(167800)^{2}}}\exp[-\frac{(x-30457500)^{2}}{2(167800)^{2}}]$

(a) To answer this question, we should to compute the next probability $P(X\geq 30000000)$ , i.e., the probability that the cycles of a bearing is equal or greater than 30,000,000.

$P(X\geq 30000000) = \int\limits_{30000000}^{\infty}f(x)dx = 0.9968$ . So,

99.68% of the bearings will last for 30,000,000 cycles.

pnorm(30000000, mean = 30457500, sd = 167800, lower.tail = FALSE) (execute this in the R statistical programming language)

(b) We are looking for a value $x_{0}$ such that

$P(X\leq x_{0}) = \int\limits_{-\infty}^{x_{0}}f(x)dx = 0.05$ and this value is $x_{0}$ = 30,181,494 cycles, i.e., we found the 5th percentile.

qnorm(0.05, mean = 30457500, sd = 167800) (execute this in the R statistical programming language)

You can use a table from a book to compute this figures or a programming language like the R statistical programming language.

Answer from: Quest

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

Answer from: Quest

$x=2\sqrt{10}$

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

$6^2+2^2=x^2$

simplifying:

$6^2+2^2=x^2\\36+4=x^2\\40=x^2\\x=\sqrt{40}$

to further simplify this radical, we need to use the property $\sqrt{x*y}=\sqrt{x} \sqrt{y}$

thus

$x=\sqrt{40}\\ x=\sqrt{4}\sqrt{10} \\ x=2\sqrt{10}$

What is the value of x? leave your answer in simplest radical form.

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2. you have tested bearings for a particular machine. this resulted in a mean of 30,457,500 cycles w...