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stich3 [128]
3 years ago
8

A quality-control inspector is testing a batch of printed circuit boards to see wheater they are capable of performing in a high

temperature environment. He knows that the boards that will survive will pass all five of the tests with probability 98%. They will pass at least four tests with probability 99%, and they always pass at least three. On the other hand, the boards that will not survive sometimes pass the tests as well. In fact, 2% pass all five tests, and another 20% pass exactly four. The rest pass at most three tests. The inspector decides that if a board passes all five tests, he will classify it as "good." Otherwise, he'll classify it as "bad." The manager says that the probability of a type I error must be no larger than 0.01.
a. What does a type II error mean here?
b. What is the probability of a type II error?
Mathematics
1 answer:
avanturin [10]3 years ago
6 0

Answer:

see explaination

Step-by-step explanation:

Here the null hypothesis is that the PCB survives against the alternate that the PCB 'does not survive'. The test says that the PCB will survice if it is classified as 'good'; or, it will not survive if it is classifies as 'bad'.

a. The Type II error is the error committed when a PCB which cannot actually survive is classified as 'good'.

b. Therefore P(Type II error) = P(The PCB is classified as 'good' | PCB does not survives) = 0.03.

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3 years ago
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(a) Work out the reciprocal of 1.25
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Answer:

0.8 OR \frac{4}{5}

Step-by-step explanation:

The reciprocal of any number is the number that it multiplies by to equal 1.

The reciprocal can be found by simply converting the number into a fraction and then 'flipping' the fraction as any number multiplied by its reciprocal is 1.

E.g.

No. X/Y * Y/X (its reciprocal) = 1

\frac{x}{y} *\frac{y}{x} =\frac{xy}{xy} =1

So, to find the reciprocal of 1.25,we should first convert 1.25 to a fraction.

1.25 = 125/100

\frac{125/25}{100/25}=\frac{5}{4}

Now we just flip 5/4 to get our reciprocal:

\frac{4}{5} = 0.8

Test: 0.8 * 1.25 = 1

The reciprocal of 1.25 (\frac{5}{4}) is 0.8 (\frac{4}{5}).

Hope this helped!

8 0
3 years ago
4.37) A set of data whose histogram is extremely skewed yields a mean and standard deviation of 70 and 12, respectively. What is
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Answer:

75%

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Step-by-step explanation:

Given :

Mean = 70

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Since the data is said to be extremely skewed, we apply Chebyshev's theorem rather than the empirical rule :

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Chebyshev's theorem :

1 - 1 / k²

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k = (94 - 70) / 12 = 24 / 12 = 2

Hence, we have ;

1 - 1/2²

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Hence, The minimum proportion of observation between 46 and 94 is 75%

Between 36 and 106 :

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k = 36/12 = 3

Hence,

1 - 1/3² = 1 - 1/9 = 8/9 = 0.8888 = 88.89%

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