Respuesta :
Answer:
[tex] P(X>4)[/tex]
And we can use the cumulative distribution fucntion given by:
[tex] F(x) =\frac{x-a}{b-a} , a \leq x \leq b[/tex]
And if we use this formula with the complement rule we have:
[tex] P(X>4)= 1-P(X<4) =1- F(4) =1-\frac{4-0}{7-0}= 1-0.5714= 0.4286[/tex]
And the best option would be:
B. 0.4286
Step-by-step explanation:
Let X the random variable that represent the time that customers wait to be served at the delicastessen for a grocery store. And we know that the distribution for X is given by:
[tex] X \sim Unif( a=0, b=7)[/tex]
And we want to find the follwing probability:
[tex] P(X>4)[/tex]
And we can use the cumulative distribution fucntion given by:
[tex] F(x) =\frac{x-a}{b-a} , a \leq x \leq b[/tex]
And if we use this formula with the complement rule we have:
[tex] P(X>4)= 1-P(X<4) =1- F(4) =1-\frac{4-0}{7-0}= 1-0.5714= 0.4286[/tex]
And the best option would be:
B. 0.4286
The probability that a randomly selected customer will wait more than 4 minutes at the delicatessen is 0.4286.
Given The time that customers wait to be served at the delicatessen for a grocery store follows the uniform distribution between 0 and 7 minutes {1,2,3,4,5,6,7}.
We have to calculate probability that a randomly selected customer will wait more than 4 minutes at the delicatessen. So for more than 4 minutes their is only 3 outcomes possible {5,6,7} because the data is uniformly distributed.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability (Event) = Favorable Outcomes/Total Outcomes = x/n
Now, probability (more than 4 minute)[tex]= \frac{3}{7}[/tex]
probability (more than 4 minute)[tex]= 0.4286[/tex].
Hence the probability that a randomly selected customer will wait more than 4 minutes at the delicatessen is 0.4286.
For more details on probability follow the link:
https://brainly.com/question/795909
