A consulting agency reports that only 30\%30%30, percent of a company's website users can successfully use a certain feature of the website. Skeptical of this claim, one of the website developers takes a simple random sample of 150150150 of the company's approximately 800080008000 users and tests whether they can use the feature successfully. The developer finds that 36\%36%36, percent of the sampled users use the feature successfully.

Assuming the agency's 30\%30%30, percent claim is correct, what is the approximate probability that more than 36\%36%36, percent of the sample would use the feature successfully?

Answer:

.36

.05

Explanation:

1) The probability  is 0.0076

2) The probability is 0.2775

3) Yes it is reasonable because it indicates is that the igniters are more successful than already thought or it would be close to impossible to get those same results by chance.

1) We are told that the overall failure rate which is the percent of all igniters that fail to operate correctly is 15 percent = 0.15\.

Thus, percentage of success = 85% = 0.85

The probability that the first 30 super igniters selected using the testing process successfully launch rockets is P(X = 30) = (0.85)³⁰

= 0.0076

2) Given that the first 30 super igniters successfully launch rockets, the probability that the 1st failure occurs on the 31st or the 32nd super igniter tested if the failure rate of the super igniters is 15 percent is;

P(Y = 31)/P(X = 30) + P(Y = 32)/P(X = 30)

= [(0.15 * 0.85³⁰)/0.85³⁰] + [(0.15 * 0.85³¹)/0.85³⁰]

= 0.2775

The probability in answer 1 above indicates is that the igniters are more successful than already thought or it would be close to impossible to get those same results by chance.

Therefore, 1) The probability  is 0.0076

2) The probability is 0.2775

3) Yes it is reasonable because it indicates is that the igniters are more successful than already thought or it would be close to impossible to get those same results by chance.

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Give two differences between Artificial and Natural Selection.

All of the following are stereotypes associated with mental illness except __________.
A.
the idea that mental illness is incurable
B.
a response of anger toward someone with a mental illness
C.
the belief that individuals with mental illness are dangerous
D.
the thought that all individuals with a mental illness are not capable of living independently

Refer to the passage.

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Sir John French, commander in chief of the British Expeditionary Force (BEF), 1915

Which of the following novel aspects of World War I contributed to the action described in the passage?

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The capability of British tanks to repel machine-gun fire
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The half-life of carbon-14 is about 5700 years. If you left those 100 carbon-14 atoms to sit around for 5700 years, how many would you expect to decay during that time?