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L15.2082 - Statistics for Business and Economics (2024/2025)
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A repair team is responsible for a stretch of oil pipeline 4 km long. The distance (in km) at which any fracture occurs, can be represented by a uniformly distributed random variable, with probability density function f(x) = 0.25. Find the probability that a fracture occurs between 0.9 km and 1.4 km.
A probability density function (PDF) cannot take values greater than 1.
Peter's score on his midterm exam was at the 50th percentile. The grades were normally distributed. The exam average was 71 and the standard deviation was 5. What was Peter's score on the exam?
A manufacturer of microwave ovens is trying to determine the length of warranty period it should attach to its magnetron tube, the most critical component in the oven. Preliminary testing has shown that the length of life (in years), X, of a magnetron tube has an exponential probability distribution with mean 6.25.
Suppose a warranty period of five years is attached to the magnetron tube. What fraction of tubes must the manufacturer plan to replace, assuming that the exponential model with mean = 6.25 is correct?A manufacturer of microwave ovens is trying to determine the length of warranty period it should attach to its magnetron tube, the most critical component in the oven. Preliminary testing has shown that the length of life (in years), X, of a magnetron tube has an exponential probability distribution with mean 6.25.
What should the warranty period be if the manufacturer wants to replace only 27.5% of the tubes?Checkout times in a grocery store follow the exponential distribution with a mean time of 6.5 minutes. What is the probability that the checkout time (T) for the next customer will be less than 5 minutes?
It has been observed that the average number of traffic accidents on the Hollywood Freeway between 7 and 8 PM on Wednesdays is 1 per hour.
Let X be defined as "the number of traffic accidents on the Hollywood Freeway between 7 and 8 PM on Wednesday".
What is the variance of X?
Suppose we know that births in a hospital occur randomly at an average rate of 1.8 births per hour.
What is the probability that we observe 5 births in a given 2 hour interval? Write your answer with 2 decimal places.
Based on past experience, it is assumed that the number of flaws per foot in rolls of grade-2 paper follows a Poisson distribution with mean of 1 flaw per 5 feet of paper.
What is the probability that in a 15-foot roll there will be at least 1 flaw?