Eli Whitney invented the the cotten gin
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.
Have you never added 2-digit numbers?
35 +27 = (30 +20) +(5 +7) = 50 +12 = 62
35/100 +27/100 = (35 +27)/100 = 62/100
0.35 +0.27 = 0.62
The basic idea, taught in 3rd grade, is to line up the decimal points of the numbers, add enough zeros on the right to make the numbers all have the same number of digits to the right of the decimal point, then add in the usual way. The sum has the decimal point aligned with the rest of the numbers.
35 +27 = (30 +20) +(5 +7) = 50 +12 = 62
35/100 +27/100 = (35 +27)/100 = 62/100
0.35 +0.27 = 0.62
The basic idea, taught in 3rd grade, is to line up the decimal points of the numbers, add enough zeros on the right to make the numbers all have the same number of digits to the right of the decimal point, then add in the usual way. The sum has the decimal point aligned with the rest of the numbers.