Aprofessional soccer player succeeds in scoring a goal on 84% of his penalty kicks. assume that the success of each kick is independent. (a) in a series of games, what is the probability that the first time he fails to score a goal is on his fifth penalty kick? (b) what is the probability that he scores on 5 or fewer of his next 10 penalty kicks? (c) suppose that our soccer player is out of action with an injury for several weeks. when he returns, he only scores on 5 of his next 10 penalty kicks. is this evidence that his success rate is now less than 84%? explain.

A. Using the geometric probability:  .84^4 * (1-.84) = 0.07966; this means that the probability that he makes his first * the probability he makes his second * the probability he makes his third * the probability he makes his fourth * the probability he misses his fifth. 

b. P (X<= 5) = binomcdf (10, 0.84, 5) = 0.0130

c. From the answer in B, if the success rate of the player still continues at 84%, the probability that he will score 5 or few goals in the 10 penalty kicks will still remain at 0.0130. This is quite low, we should examine him about whether he can still hit at 84% of his shots. So given from this data, we could say that his penalty kick success rate has fallen below the given rate of 84%.

Geometric Distributions:Deals with the number of trials required until a single success.
 Geometric random variable: the number of trials (y) it takes to get a success in a geometric setting.
 When do you use it? To find first success or failure
 Calculator Commands
 When it takes more than n trials...1-geometcdf(p,n)
 When it take n trials... geometpdf(p,x)
 When it it takes a max of n trials...geometcdf(p,x)
 a. geometcdf(.16,5) = .0797
 b. binomcdf(10,.84,5) = .013
 c. From par b. if the soccer player's succes rate were still 84%, the probability that he would score 5 or few goals in 10 penalty kicks is 0.0130. This is so low thatwe should be suspicious about whether he can still hit 84% of his shots. We have convincing that his penalty kick success rate has fallen below 84%

The radiation of the fire causes the saucepan to heat up. the conduction of the saucepan then to distribute the heat over the saucepan and to give heat to the water. the convection of the water distributing the heat within the water, till all the water is boiling

Answer(b) 60 miles per hour;