snurpeisov
07.10.2020 •
Mathematics
Suppose that the following frequency table contains data on the number of absences in a school year due to illness or injury for 100 randomly selected high school students. Use the table to determine the median number of absences for these 100 students. Provide your answer with precision to one decimal place.
Number of absences 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Frequency 25, 10, 10, 5, 9, 12, 9, 9, 4, 2, 3, 2
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Ответ:
a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?
We want this probability"
At most 3 hours?
b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?
What is the probability that it is less than the mean value by more than one standard deviation?
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
The cumulative distribution for this function is given by:
We know the value for the mean on this case we have that :
Solution to the problem
Part a
What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?
We want this probability"
At most 3 hours?
Part b
What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?
The variance for the esponential distribution is given by:
And the deviation would be:
And the mean is given by
Two deviations correspond to 5.540, so we want this probability:
What is the probability that it is less than the mean value by more than one standard deviation?
For this case we want this probablity: