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1 answer:
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Answer:
(a) The mean is 107.25, median is 106 and mode is 95.
(b) The data set is right-skewed.
Step-by-step explanation:
The sample space of amount spent for dinner for 28 four-person tables is:
S = {95, 103, 109, 170, 114, 113, 107, 124, 105, 80, 104, 84, 176, 115, 69, 95, 134, 108, 61, 160, 128, 68, 95, 61, 150, 52, 87, 136}
There are <em>n</em> = 28 values in the set.
(a)
The mean of this data set is:
The mean is 107.25.
The data set consists of even number of observations.
The median for an even set of data is the mean of the middle two numbers.
First arrange the data set in ascending order:
52, 61 , 61 , 68 , 69 , 80 , 84 , 87 , 95 , 95 , 95 , 103 , 104 , 105 , 107 , 108 , 109 , 113 , 114 , 115 , 124 , 128 , 134 , 136 , 150 , 160 , 170 , 176
The median is the average value of the 14th and 15th observation.
The median is 106.
The mode of a data set is the value with the most frequency.
Consider the arranged data set.
52, 61 , 61 , 68 , 69 , 80 , 84 , 87 , 95 , 95 , 95 , 103 , 104 , 105 , 107 , 108 , 109 , 113 , 114 , 115 , 124 , 128 , 134 , 136 , 150 , 160 , 170 , 176
The value 95 is repeated most of the times.
Thus, the mode is 95.
(b)
The value of mean, median and mode are related as follows:
Mean > Median > Mode
This implies that the data is skewed.
In case of a right-skewed data the Mean > Median > Mode.
In case of left skewed data the Mean < Median < Mode.
Thus, the data set is right-skewed.
Answer:
a.
b.
c.
No, it is not unusual if at least 1 lives up to 3.
Step-by-step explanation:
Given
Represent the probability that a 2 year old snake will live to 3 with P(Live);
Solving (a): Probability that two selected will live to 3 years.
Both snakes have a chance of 0.98861 to live up to 3 years.
So, the required probability is:
<em>--- Approximated</em>
Solving (b): Probability that seven selected will live to 3 years.
All 7 snakes have a chance of 0.98861 to live up to 3 years.
So, the required probability is:
Where
<em>--- Approximated</em>
Solving (c): Probability that at least one of seven selected will not live to 3 years.
In probabilities, the following relationship exist:
So, first we need to calculate the probability that none of the 7 lived up to 3.
If the probability that one lived up to 3 years is 0.98861, then the probability than one do not live up to 3 years is 1 - 0.98861
This gives:
The probability that none of the 7 lives up to 3 is:
Substitute this value for P(None) in
---- Approximated
No, it is not unusual if at least 1 lives up to 3.
This is so because the above results, which is 1 shows that it is very likely for at least one of the seven to live up to 3 years