Complete this expression using the distributive property
1 answer:
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Answer:
The lower bound of the probability that there will be between 100 and 140 passengers 96%.
Step-by-step explanation:
The Chebyshev's theorem states that, the probability that <em>X</em> is within <em>k</em> standard deviation of mean is given by,
Here, k is any positive number.
The given information is:
Mean (<em>µ</em>) = 120
Standard deviation (<em>σ</em>) = 16.
Then, we need to compute, P (100 ≤ X ≤ 140).
Then,
Since, these two values coincide it implies that the event (66000, 78000) is centered about the mean.
Also, the event P (100 ≤ X ≤ 140) is equivalent to having X within 5 standard deviation of the mean.
That is, <em>k</em> = 5.
Then for k = 5,
That is, <em>P</em> (100 ≤ <em>X</em> ≤ 140) ≤ 0.96 .
Thus, the lower bound of the probability that there will be between 100 and 140 passengers 96%.
Answer:
The 5-number summary is maximum= 175, minimum=126, median=150, Q₁=138 and Q₃=160.5.
Step-by-step explanation:
The given data set is
126, 128, 131, 135, 136, 140, 143, 145, 147, 148, 152, 154, 155, 156, 159, 162, 164, 166, 169, 175
The minimum value of the data is 126 and the maximum value of the data is 175.
Divide the data in two equal parts.
(126, 128, 131, 135, 136, 140, 143, 145, 147, 148), (152, 154, 155, 156, 159, 162, 164, 166, 169, 175)
The median of the data is
Now divide each parenthesis in two equal parts.
(126, 128, 131, 135, 136), (140, 143, 145, 147, 148), (152, 154, 155, 156, 159), (162, 164, 166, 169, 175)
Therefore the 5-number summary is maximum= 175, minimum=126, median=150, Q₁=138 and Q₃=160.5.
