Identify the parameter n in the following binomial distribution scenario. A weighted coin has a 0.441 probability of landing on heads and a 0.559
... [Show More] probability of landing on tails. If you toss the coin 19 times, we want to know the probability of getting heads more than 5 times. (Consider a toss of heads as success in the binomial distribution.)
A softball pitcher has a 0.675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes.
Consider strikes as successes in the binomial distribution. Do not include p=
in your answer.
The probability of winning on an arcade game is 0.568. If you play the arcade game 22 times, what is the probability of winning more than 15
times?
• Round your answer to three decimal places.
This probability can be found using the binomial distribution with success probability p=0.568 and 22 trials. To find the probability that more than 15 of the games are wins, use a calculator or computer: P(X>15)=1−binomcdf(22,0.568,15)≈0.096.
A weighted coin has a 0.55 probability of landing on heads. If you toss the coin 14 times, what is the probability of getting heads exactly 9 times? (Round your answer to 3 decimal places if necessary.)
Answer Explanation
Correct answers:
This probability can be found using the binomial distribution with success probability p=0.55 and 14 trials. To find the probability that exactly 9 of the tosses are heads, use a calculator or computer:
P(X=9)=binompdf(14,0.55,9)≈0.170.
Consider how the following scenario could be modeled with a binomial distribution, and answer the question that follows.
54.4% of tickets sold to a movie are sold with a popcorn coupon, and 45.6% are not. You want to calculate the probability of selling exactly 6 tickets with popcorn coupons out of 10 total tickets (or 6 successes in 10
trials).
What value should you use for the parameter p?
0 point 5 4 4$$0.5440 point 5 4 4 - correct
Answer Explanation
Correct answers:
• 0 point 5 4 4 $0.544$0.544 The parameters p and n represent the probability of success on any given
trial and the total number of trials, respectively. In this case, success is a movie ticket with a popcorn coupon, so p=0.544.
Identify the parameters p and n in the following binomial distribution scenario. The probability of winning an arcade game is 0.718 and the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)
p=0.282, n=20
p=0.718, n=15 p=0.718, n=20 p=0.282, n=15
Answer Explanation
Correct answer:
p=0.718, n=20
The parameters p and n represent the probability of success on any given
trial and the total number of trials, respectively. In this case, success is winning a game, so p=0.718. The total number of trials, or games, is n=20.
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Assignment progress: 50%
Use the binomial distribution to compute probability
Question
In a large population, about 25% of workers spend more than thirty minutes commuting to work in the morning. A researcher takes a random sample of 20 workers and surveys whether they commute for more than thirty minutes in the
morning.
Use the binomial distribution to compute the probability that exactly 11 of the workers commute for more then thirty minutes in the morning.
Identify the following information required to find the probability of commuters traveling for more than thirty minutes to work in the morning.
Answer 1:
n = 25$$2525 - incorrect trials
x = 20$$2020 - incorrect successes
p = 5$$55 - incorrect probability of more than thirty minutes commuting (as a decimal, not percent)
response - incorrect Correct answers: Answer 2:
n = 25$$2525 - incorrect trials
x = 20$$2020 - incorrect successes
p = 5$$55 - incorrect probability of more than thirty minutes commuting (as a decimal, not percent)
response - incorrect Correct answers:
Answer Explanation
n = 1$$1 - no response given trials
x = 2$$2 - no response given successes
p = 3$$3 - no response given probability of more than thirty minutes commuting (as a decimal, not percent)
Correct answers:
• 120$20$20
• 211$11$11
• 3point 2 5$.25$.25
We determine n , the number of trials, by reviewing the context. The researcher randomly sampled 20 workers.
We determine x , the number of successes, by determining what results we are looking for. In this case, we'd like to know the probability for the number of times exactly 11 workers commute more than thirty minutes in the morning.
Finally, we determine the probability from the context, as we're told about 25% of workers spend more than thirty minutes commuting to work in the morning.
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In a large population, about 25% of workers spend more than thirty minutes commuting to work in the morning. A researcher takes a random sample of 20 workers and surveys whether they commute for more than thirty minutes in the
morning.
Use the binomial distribution to compute the probability that exactly 11 of the workers commute for more then thirty minutes in the morning.
To show your answer:
1. Move the purple dots to identify the number of trials, n, and the probability of success, p.
2. Use the black dot on the x -axis to represent the number of successes and display the probability.
Answer 1:
Probability of 25 successes = 0 Number of trials
Probability of success n = 1
p = 0.35
Answer 2:
Probability of 25 successes = 0 Number of trials
Probability of success n = 1
p = 0.35
Answer Explanation
Example Correct Answer
Probability of 11 successes = 0.003 Number of trials
Probability of success n = 20
p = 0.25
Since we are counting the number of workers that spend more than thirty minutes commuting to work in the morning, and we know about 25% of all workers spend more than thirty minutes commuting to work in the morning, the probability of success is p=0.25.
Since there are 20 workers in the sample, and each worker is independent of others, we have n=20 independent trials.
The problem asks for the probability that exactly 11 of the 20 workers spend more than thirty minutes commuting to work in the morning. Using the binomial distribution, we set the purple dot sliders to p=0.25 and n=20, and we set the black dot slider to 11 to see the probability is 0.003.
Jamie is practicing free throws before her next basketball game. The probability that she makes each shot is 0.6. If she takes 10 shots, what is the probability that she makes exactly 7 of them? Round your answer to
three decimal places.
0.200
0.215
0.234
0.251
Answer Explanation
Correct answer:
0.215
For the below problem, which values would you fill in the blanks of the function binompdf( , , ) if you are using a TI-84 graphing calculator?
The probability of saving a penalty kick from the opposing team is 0.617 for a soccer goalie. If 7 penalty kicks are shot at the goal, what is the probability that the goalie will save 5 of them?
binompdf(0.617,5,7)
binompdf(5,7,0.617) binompdf(7,0.617,5) binompdf(7,5,0.617)
Answer Explanation
Correct answer:
binompdf(7,0.617,5)
The parameters of a binomial distribution are:
• n = the number of trials
• x = the number of successes in the whole experiment
• p = the probability of a success
If you are using a TI-84 graphing calculator, you must input the parameters in the order of n, p, x, into the binomial probability density
function: binompdf(n, p, x).
So, in this case, you should input binompdf(7,0.617,5).
65 % of the people in Missouri pass the driver’s test on the first attempt. A group of 7 people took the test. Which of the following equations correctly calculate the probability that at least 3 in the group pass their driver's tests in their first atempt? Select all that apply.
Remember: 65 % = 0.65.
•
P(X≥3)=P(X=3)+P(X=2)+P(X=1)+P(X=0)
•
•
P(X≥3)=P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)
•
•
P(X≥3)=1−P(X=3)
•
•
P(X≥3)=1−[P(X=2)+P(X=1)+P(X=0)]
•
Answer Explanation
Correct answer:
We need to find the probability of 3,4,5,6 , and 7 friends passing their driver's tests in their first attempt.
There are two different ways to find this probability:
1. Sum the probabilities of each case.
2. Find the probability of 0,1 , and 2 friends passing their driver's tests in their first attempt. Add the probabilities and subtract the sum from 1 to use the cumulative rule.
Your answer:
P(X≥3)=P(X=3)+P(X=2)+P(X=1)+P(X=0)
The equation is wrong. The right hand side of this equation calculates P(X≤3) .
P(X≥3)=1−P(X=3)
The equation is wrong. The right hand side of this equation calculates P(X≠3) or
P(X=0)+P(X=1)+P(X=2)+P(X=4)+P(X=5)+P(X=6)+P(X=7) [Show Less]