What is a solution to (x + 6)(x + 2) = 60?
1 answer:
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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.
Answer:
The probability of a selected car being a 4 door car, given that the car has a sunroof = 0.40
Step-by-step explanation:
The complete question is presented in the attached image.
The conditional probability, of event A happening, given that event B has happened, P(A|B), is given mathematically as
P(A|B) = P(A n B) ÷ P(B)
So, the required probability of a selected car being a 4 door car, given that the car has a sunroof is given as
P (4 doors | sunroof)
= P (4 doors n sunroof) ÷ P(sunroof)
Note that the probability of an event is given as the number of elements in that event divided by the Total number of events.
P (4 doors n sunroof)
= n (4 doors n sunroof) ÷ n (total)
From the Venn Diagram in the attached image,
n (4 doors n sunroof) = 20 + 0 = 20
n (total) = 100
P (4 doors n sunroof) = (20/100) = 0.20
P(sunroof) = n(sunroof) ÷ n(total)
n(sunroof) = 12 + 18 + 20 + 0 = 50
n(total) = 100
P(sunroof) = (50/100) = 0.50
P (4 doors | sunroof)
= P (4 doors n sunroof) ÷ P(sunroof)
= (0.20/0.50) = 0.40
Hope this Helps!!!
