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portielesc
09.10.2019 •
Mathematics
Wires manufactured for use in a computer system are specified to have resistances between .12 and .14 ohms. the actual measured resistances of wires produced by company a have a normal probability distribution with mean .13 ohm and standard deviation .005 ohm. a. (15 pts) what is the probability that a randomly selected wire from company a’s production will meet the specifications? z = (x-µ)/σ p(x< .12) = p(z< ( (.12- .14)/.005) = b. (10 pts) if four of these wires are used in each computer system and all are selected from company a. what is the probability that all four in a randomly selected system will meet the specifications?
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Ответ:
a) 0.9544996
b) 0.9999366
Step-by-step explanation:
Given : The actual measured resistances of wires produced by company A have a normal probability distribution with mean
ohm and standard deviation
ohm.
Wires manufactured for use in a computer system are specified to have resistances between .12 and .14 ohms.
Let x be the random variable that represents the value of resistance in wires.
Using formula for z-score ,![z=\dfrac{x-\mu}{s}](/tpl/images/0304/3427/84011.png)
The z-value at x= 0.12 will be
The z-value at x= 0.14 will be
The p-value :![P(-2](/tpl/images/0304/3427/a7257.png)
Hence, the probability that a randomly selected wire from company A’s production will meet the specifications = 0.9544996
b) Sample size : n= 4
Using formula for z-score ,![z=\dfrac{x-\mu}{\dfrac{s}{\sqrt{n}}}](/tpl/images/0304/3427/a4cd7.png)
The z-value at x= 0.12 will be
The z-value at x= 0.14 will be
The p-value :![P(-4](/tpl/images/0304/3427/a0a12.png)
The probability that all four in a randomly selected system will meet the specifications = 0.9999366
Ответ:
10500 dollars
Step-by-step explanation:
350,000 * .03 = 10500