Chips Ahoy! 1,000 Chips Challenge. Students in an introductory statistics course at the U.S. Air Force Academy participated in Nabisco's challenge by confirming that there were at least 1000 chips in every 18-ounce bag of cookies that they examined. As part of their assignment, they concluded that the number of chips per bag is approximately normally distributed. [SOURCE: Brad Warner and Jim Rutledge, "Checking the Chips Ahoy! Guarantee," Chance, 1999, Vol. 12(1), pp. 10-14] Could the number of chips per bag be exactly normally distributed? Explain your answer. Assume that μ = 1000 and σ = 16. What is the probability of the bag containing between 950 and 1025 chips? Assume that μ = 1000 and σ = 16. What is the z-score associated with 982 chips? Is there enough information to simulate 500 observations of the variable x for chips in a bag? If yes then show and explain your results; otherwise, explain what additional information is needed.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Chips Ahoy! 1,000 Chips Challenge. Students in an introductory statistics course at the U.S. Air Force Academy participated in Nabisco's challenge by confirming that there were at least 1000 chips in every 18-ounce bag of cookies that they examined. As part of their assignment, they concluded that the number of chips per bag is approximately
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- Could the number of chips per bag be exactly normally distributed? Explain your answer.
- Assume that μ = 1000 and σ = 16. What is the
probability of the bag containing between 950 and 1025 chips? - Assume that μ = 1000 and σ = 16. What is the z-score associated with 982 chips?
- Is there enough information to simulate 500 observations of the variable x for chips in a bag? If yes then show and explain your results; otherwise, explain what additional information is needed.
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