Could use help, know the answers but with the process and equations

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SUMMARY

This discussion focuses on various probability problems and concepts related to normal distribution and independent events. Key examples include calculating the percentage of data within a range for a normally distributed set with a mean of 25 and standard deviation of 2, and determining the probability of events A and B occurring independently. The conversation also addresses practical applications of probability in real-world scenarios, such as customer advertisement exposure and equipment defects from different factories.

PREREQUISITES
  • Understanding of normal distribution concepts
  • Familiarity with basic probability theory
  • Knowledge of independent and dependent events
  • Ability to perform calculations involving means and standard deviations
NEXT STEPS
  • Explore the use of normal distribution calculators for statistical analysis
  • Learn about the Central Limit Theorem and its implications in statistics
  • Study conditional probability and its applications in real-world scenarios
  • Investigate the differences between discrete and continuous probability distributions
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Students, statisticians, data analysts, and anyone interested in mastering probability theory and its applications in various fields.

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A normally distributed data set has a mean of 25 and a standard deviation of 2.
Which percentage of the data falls between 23 and 25?

A given data set is normally distributed with a mean of 200 and a standard deviation of 5.
Which two values does 95% of the data fall between?

A
and B are events associated with an experiment with P( A) = .3 and P( B) = .5.
If A and B are independent, then what is the probability that A or B occurs?

A six-sided die, with a number from 1 to 6 on each side, is rolled twice.
What is the probability that two odd numbers are rolled consecutively?

A fast-food company is interested in knowing the probability of whether a customer viewed an advertisement for their new special on the internet or on television. They found that 37% of customers saw the advertisement on the internet, 20% saw it on television, and 12% saw it on both the internet and on television.
What is the probability that a randomly selected customer saw the advertisement on the internet or on television?

The probability of a breakdown on assembly line A is 12%. The probability of a breakdown on assembly line B is 16%. The probability that both assembly lines break down is 2%.
What is the probability that assembly line A or assembly line B break down?

An old piano has 88 keys, and 56 of them are out of tune, while the remaining keys are tuned properly. A child strikes a key on the piano at random.
What is the probability that the child strikes a properly tuned key?

A marketing company chooses a survey participant among two respondents: one female and one male. The chosen participant is then asked to rate either product A, B, or C.
What is the probability that the respondent was male and rated product B?

A bag contains 8 red, 4 green, and 9 blue marbles. One marble is drawn from the bag, not replaced, and then a second marble is drawn.
Which statement is always correct?

A company receives equipment from two factories: 38% from factory A, and all other equipment from factory B. Each factory has a percentage of equipment that is defective: 1% of factory A's equipment is defective, while 4% of factory B's equipment is defective.
If a piece of the company's equipment is selected at random, what is the probability that it is defective and from factory B?

A box contains one red ball, one purple ball, and one blue ball. Two balls are drawn from the box one after the other without replacing the first ball.
How many outcomes are possible for this experiment?
 
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Where did you get these? They are all fairly basic problems. Have you not at least tried something?
 

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