What is the area of the triangle?
2 answers:
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Answer:
(a) P (X = 0) = 0.0498.
(b) P (X > 5) = 0.084.
(c) P (X = 3) = 0.09.
(d) P (X ≤ 1) = 0.5578
Step-by-step explanation:
Let <em>X</em> = number of telephone calls.
The average number of calls per minute is, <em>λ</em> = 3.0.
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 3.0.
The probability mass function of a Poisson distribution is:
(a)
Compute the probability of <em>X</em> = 0 as follows:
Thus, the probability that there will be no calls during a one-minute interval is 0.0498.
(b)
If the operator is unable to handle the calls in any given minute, then this implies that the operator receives more than 5 calls in a minute.
Compute the probability of <em>X</em> > 5 as follows:
P (X > 5) = 1 - P (X ≤ 5)
Thus, the probability that the operator will be unable to handle the calls in any one-minute period is 0.084.
(c)
The average number of calls in two minutes is, 2 × 3 = 6.
Compute the value of <em>X</em> = 3 as follows:
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Thus, the probability that exactly three calls will arrive in a two-minute interval is 0.09.
(d)
The average number of calls in 30 seconds is, 3 ÷ 2 = 1.5.
Compute the probability of <em>X</em> ≤ 1 as follows:
P (X ≤ 1 ) = P (X = 0) + P (X = 1)
Thus, the probability that one or fewer calls will arrive in a 30-second interval is 0.5578.
Answer:
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Step-by-step explanation:
The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. We can write the null hypothesis in the form
In this context, the investigator's null hypothesis should be that the average total weight is no different than the reported value by the FAA. We can write it in this form .
The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. We can write the alternative hypothesis in one of three forms
The investigator wants to know if the average weight of passengers flying on small planes exceeds the FAA guideline of the average total weight of 185 pounds. He should use as his alternative hypothesis.