Mr. Hammond is the volunteer coordinator for a company that puts on running races. Last year, the company organized 7 short race
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Hi, you've asked an incomplete question. Here are the remaining questions:
a) Describe what each region in the Venn diagram represents.
Region I: In drama club, not in step team.
Region II: In both clubs.
Region III: In step team not in drama.
Region IV: Not in either club.
b) How many students were in only one of the two clubs?
c) How many students were in the drama club or in the step team?
d) How many students were surveyed?
Attached is the Venn diagram depicting the regions.
Explanation:
b) By adding the number of students that like drama club and those that like step club we can derive the answer: 34 + 27 = 61.
c) By adding 34 + 27 + those that like both (14) = 75.
d) The total number of students surveyed is gotten by summing any number in attached the diagram: 34 + 27 + 14 + 13 = 88.
Answer:
Part a: <em>The probability of no arrivals in a one-minute period is 0.000045.</em>
Part b: <em>The probability of three or fewer passengers arrive in a one-minute period is 0.0103.</em>
Part c: <em>The probability of no arrivals in a 15-second is 0.0821.</em>
Part d: <em>The probability of at least one arrival in a 15-second period is 0.9179.</em>
Step-by-step explanation:
Airline passengers are arriving at an airport independently. The mean arrival rate is 10 passengers per minute. Consider the random variable X to represent the number of passengers arriving per minute. The random variable X follows a Poisson distribution. That is,
The probability mass function of X can be written as,
Substitute the value of λ=10 in the formula as,
Part a:
The probability that there are no arrivals in one minute is calculated by substituting x = 0 in the formula as,
<em>The probability of no arrivals in a one-minute period is 0.000045.</em>
Part b:
The probability mass function of X can be written as,
The probability of the arrival of three or fewer passengers in one minute is calculated by substituting \lambda = 10λ=10 and x = 0,1,2,3x=0,1,2,3 in the formula as,
<em>The probability of three or fewer passengers arrive in a one-minute period is 0.0103.</em>
Part c:
Consider the random variable Y to denote the passengers arriving in 15 seconds. This means that the random variable Y can be defined as
That is,
So, the probability mass function of Y is,
The probability that there are no arrivals in the 15-second period can be calculated by substituting the value of (λ=2.5) and y as 0 as:
<em>The probability of no arrivals in a 15-second is 0.0821.</em>
Part d:
The probability that there is at least one arrival in a 15-second period is calculated as,
<em>The probability of at least one arrival in a 15-second period is 0.9179.</em>