Question

In: Statistics and Probability

1 The number of goals in a World Cup soccer match has a Poisson distribution with...

1

The number of goals in a World Cup soccer match has a Poisson distribution with a mean of 3. For a soccer player in World Cup, the probability of having an age over 30 is 0.2.

a. What is the probability of having 0 goal in a World Cup soccer match? (3 pts) What is the probability of having more than 1 goal in a World Cup soccer match?

b. What is the probability that 0 out of the 11 players in a World Cup soccer team are older than 30 ?

c. The probability that a soccer team wins a World Cup match is 0.7 if none of its players are older than 30. The probability that a soccer team wins a World Cup match is 0.4 if some players are older than 30. The probability that “no players are older than 30 in a World Cup soccer team” is your result from question b. A soccer team just won the latest World Cup match. Given this information, what is the probability that NO players in the team have an age over 30?

Expert Solution

The Answers

Answer a:

Probability of scoring 0 goals in the match = 0.0498

Probability of scoring more than 1 goal in the match = 0.8008

Answer b:

Probability that 0 out of 11 players in the team are older than 30 = 0.0859

Answer c:

Given that , a team has won the match ,

Probability that NO players in the team have an age over 30 = 0.6364

(All the Answers are rounded up to 4 decimal places)

orchestra answered 1 year ago

Penalty Shots in World Cup Soccer A study1 of 138 penalty shots in World Cup Finals...

Penalty Shots in World Cup Soccer A study1 of 138 penalty shots in World Cup Finals games between 1982 and 1994 found that the goalkeeper correctly guessed the direction of the kick only of the time. The article notes that this is ‘‘slightly worse than random chance.” We use these data as a sample of all World Cup penalty shots ever. Test at a significance level to see whether there is evidence that the percent guessed correctly is less than...

1. The number of raisins in buns has Poisson distribution with an average of 5 raisins...

1. The number of raisins in buns has Poisson distribution with an average of 5 raisins per bun. a) Bob buys a bun every day. What is the expected number of buns he buys before he finds a bun with no raisins at all? b) Joe bought a bun for breakfast and cut it into two equal parts. What is the probability that at least one of these parts has no raisins in it? c) Emily bought seven buns in...

The number of imperfections in an object has a Poisson distribution with a mean λ =...

The number of imperfections in an object has a Poisson distribution with a mean λ = 8.5. If the number of imperfections is 4 or less, the object is called "top quality." If the number of imperfections is between 5 and 8 inclusive, the object is called "good quality." If the number of imperfections is between 9 and 12 inclusive, the object is called "normal quality." If the number of imperfections is 13 or more, the object is called "bad...

A study of 36 forwards in soccer showed that their average number of goals in a...

A study of 36 forwards in soccer showed that their average number of goals in a season was 12 with a standard deviation of 2. Construct the confidence interval for the average number of goals in a season. Remember to put the numbers in the formula first and then use the calculator to compute the confidence interval.

Suppose that Y is the Poisson distribution of the number of students a school has. Find...

Suppose that Y is the Poisson distribution of the number of students a school has. Find the mode by studying the monotonicity and explaining if the mean is a)5.3 and other case b) 6

Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆.

Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆. To estimate 𝜆 we obtain the random sample 𝑋1,𝑋2, … , 𝑋n.a. Find the Fisher information is a single observation using two methods.b. Find the Cramer-Rao lower bound for the variance of an unbiased estimator of 𝜆.c. Find the MLE of 𝜆 and show that the MLE is an efficient estimator.

Q3. (a) The number of knots in a particular type of wood has a Poisson distribution...

Q3. (a) The number of knots in a particular type of wood has a Poisson distribution with an average of 1.5 knots in 0.28m3 of the wood. Find the probability that a 0.28m3 block of the wood has at most 1 knot. [3] (b) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car arrives during...

The number of errors in each of 300 files has a Poisson distribution with 1.4 errors...

The number of errors in each of 300 files has a Poisson distribution with 1.4 errors per file on average. Assume the errors in different files are independent. Use the Central Limit Theorem to approximate the probability that the total number of errors is at least 400. (Use a calculator.)

The heights (in centimeters) of some randomly selected Men's World Cup soccer players from both Europe...

The heights (in centimeters) of some randomly selected Men's World Cup soccer players from both Europe and the U.S. are given in the table below. Europe 169 170 171 175 175 175 178 180 181 182 184 185 185 187 189 United States 167 168 169 173 176 176 178 180 180 181 183 183 186 187 187 Is there a difference between the heights of European and American soccer players? Show all 5 steps, including critical value and p-value.

The number of arriving customers to a big supermarket is following a Poisson distribution with a...

The number of arriving customers to a big supermarket is following a Poisson distribution with a rate of 4 customers per a minute. What is the probability that no customer will arrive in a given minute? What is the probability that exactly 3 customers will arrive in a given minute? What is the probability that at least seven customer will arrive in a given minute? What is the probability that at most one customer will arrive in 40 seconds? What...