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Binomial Distribution Problem Statement ...
| Binomial Distribution | |||||
| Problem Statement | |||||
| A common example of a binomial distribution is the tossing of a coin and counting the number of heads. For example, what is the probability of 4 heads in 5 tosses of a coin given the probability of heads is 50%? | |||||
| Number of trials (n) | |||||
| Probability of success (p) | |||||
| Number of successes (r) | |||||
| Expected Value | |||||
| Variance | |||||
| P(x = r) | |||||
| P(x <= r) | |||||
| Normal Distribution | |||||
| Problem Statement | |||||
| A maintenance facility's meant time to complete an aircraft inspection is 100 hours with a standard deviation of 15 hours. The facility agreed to a contract to provide aircraft inspections in 130 hours for a large commuter fleet. What is the probability the facility will meet the contract? | |||||
| mean (μ) | |||||
| Standard deviation (σ) | |||||
| Random variable to measure (X) | |||||
| Z | |||||
| P(x = X) | |||||
| P(x < X) | |||||
| F Distribution | |||||
| Problem Statement | |||||
| The F statistic is the ratio of two sample variances. Every F distribution had degrees of freedom for the numerator (df1) and denominator (df2) of the ratio. To find the F value that is associated with a particular probability and degrees of freedom, we use the following methods. In this example, df1 = 5, df2 = 6, and the probability is 0.05. The calculated f for the second part is 4.3874 | |||||
| To find F given α | |||||
| Numerator df1 | |||||
| Denominator df2 | |||||
| Probability (α) | |||||
| F-value | |||||
| To find the probability to the right of a calculated value, f | |||||
| Numerator df1 | |||||
| Denominator df2 | |||||
| f | |||||
| F-value | |||||
| Exponential Distribution | |||||
| Problem Statement | |||||
| A ground crew can unload passenger bags from a 737 at a rate of about three aircraft per hour and the service time is exponentially distributed. What is the probability that the time to unload an aircraft will be 1/2 hour or less? | |||||
| Avg # processed in period (μ) | |||||
| Time (t) | |||||
| P(t < X) | |||||
| P(X <= t) | |||||
| Poisson Distribution | |||||
| Problem Statement | |||||
| Commuter aircraft arrive to Gate 10 on average twice per hour. What is the probability that two aircraft with arrive to Gate 10 in an hour? | |||||
| Avg # of arrivals per unit of time (λ) | |||||
| Number of occurrences (x) | |||||
| P(x = X) | |||||
| P(x < X) | |||||
| Result Statements | |||||
| Note: Write result statements that concisely presents all of the information in a recommendation format. | |||||
| Answer the questions to two decimal places (e.g., x.xx). | |||||
| 1. what is the probability of 4 heads in 5 tosses of a coin given the probability of heads is 50%? | |||||
| 2. What is the probability the facility will meet the contract? | |||||
| 3. What is the F value given the probability? | |||||
| 4. What is the probability to the right of the f value determined in the previous question? | |||||
| 5. What is the probability that the time to unload an aircraft will be 1/2 hour or less? | |||||
| 6. What is the probability that two aircraft with arrive to Gate 10 in an hour? | |||||
Answer & Explanation
Solved by verified expertAnswered by PresidentTapirPerson768 on coursehero.com
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