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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answered: 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.

answered: Guest

I'm not sure exactly but my best guess would be 1/4

answered: Guest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

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