Ayaana Buck
2021-01-02
Nathalie Redfern
Skilled2021-01-03Added 99 answers
Given:
*The interval of the uniform distribution is
a) If the function has a uniform distribution on the interval, the mean depth is,
cm
The depth's variance is determined by:
cm
b)
The cdf or cumulative distribution function of the depth is given by:
c)
Given is the probability that the observed depth is at most 10:
The probability that observed depth is in between 10 and 15 is given by:
Substitute the values in the above expression.
Therefore, the probability that observed depth is in between 10 and 15 is given by:
d) The limit within one deviation from the mean is,
The probability that the observed depth is within 1 standard deviation of the mean value is given by:
Substitute the values in the above expression.
Hence, the probability that the observed depth is within 1 standard deviation of the mean value is,
The limit within two deviation from the mean is,
But the random variable is defined on the interval [7.5 and 20]
Hence, If the observed depth is within 2 standard deviations of the mean value, the probability is,
Substitute the values in the above expression.
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