An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up?

the probability that there will be a seat available for every passenger who shows up is 0.74

Step-by-step explanation:

if the probability of choosing a passenger that will not show up is 5% , then the probability of choosing a passenger that will show up is 95%.

Denoting event X= x passengers will show up from the total of 52 that purchased the ticket

Then P(X) follows a binomial probability distribution, since each passenger is independent from others. Thus

P(X) = n!/((n-x)!*x!)*p^x*(1-p)^(n-x)

where

n= total number of passengers hat purchased the ticket= 52

p= probability of choosing a passenger that will show up

x = number of passengers that will show up

therefore the probability that the number does not exceed the limit of 50 passengers is:

P(X≤50)=  ∑P(X=i)  from i=0 to i=50   =F(50)

where F(x) is the cumulative binomial probability distribution, then from tables:

P(X≤50)= F(50) = 0.74

therefore the probability that there will be a seat available for every passenger who shows up is 0.74

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.