8. Multiply the following numbers using scientific notation: (2 x 10^3)(2 x 10^4).
1 answer:
Answer:
<h2><u>Question 8 </u></h2>Multiply the following numbers using scientific notation: (2 x 10^3)(2 x 10^4).
(2 x 10^3) = 2*10*10*10 = 2000
(2 x 10^4) = 2*10*10*10*10 = 20000
2000*20000
=40 000 000
=
Divide the following numbers using scientific notation: (4 x 10^2)/(1 x 10^3)
(4 x 10^2) = 4*10*10 = 400
(1 x 10^3) = 1*10*10*10= 1000
400/1000 = 0.4
=
Perform the following calculation: (1 x 10^2)(2 x 10^3)/(1 x 10^2)
(1 x 10^2) = 1*10*10= 100
(2 x 10^3) = 2*10*10*10 =2000
100*2000 = 200 000
(1 x 10^2) = 1*10*10 = 100
200 000/100 = 2000
=
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Answer:
We conclude that this is an unusually high number of faulty modems.
Step-by-step explanation:
We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.
The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.
Let p = <em><u>population proportion</u></em>.
So, Null Hypothesis, : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}
Alternate Hypothesis, : p > 0.013 {means that this is an unusually high number of faulty modems}
The test statistics that would be used here <u>One-sample z-test</u> for proportions;
T.S. = ~ N(0,1)
where, = sample proportion faulty modems=
= 0.027
n = sample of modems = 367
So, <u><em>the test statistics</em></u> =
= 2.367
The value of z-test statistics is 2.367.
Since, we are not given with the level of significance so we assume it to be 5%. <u>Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.</u>
Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.
Therefore, we conclude that this is an unusually high number of faulty modems.