Jacob’s daily tips this work week were $99, $78, $58, $91, $90, and $68. Is Jacob correct in thinking that the median best repre
2 answers:
Option d: Yes, Jacob is correct. The median amount he makes is $84.00 in a day.
Explanation:
It is given that Jacob's daily tips for week are $99, $78, $58, $91, $90, and $68.
We need to determine the median of how much money he makes in daily tips.
Thus, to determine the median, first let us arrange the tips in ascending order.
Ascending order: $58, $68, $78, $90, $91 and $99
Since, the group is an even number of terms, let us add the two middle terms and divide by 2.
Median =
Thus, the median is 84.
Hence, The median amount Jacob makes is $84.00 in a day.
Thus, Option d is the correct answer.
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Answer:
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: