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Answer:
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Step-by-step explanation:
1. The percentage of the players who finished the walk in less than 2 hours will be 2.28%
2. The probability that two randomly chosen players completed the walk in 2.9 hours or more was 15.87%
3. The probability that four randomly chosen players completed the walk was between 1.7 and 2.9 hours 84%
4. The number of participants who complete the walk in more than 3.5 hours, given that there are 1,200 participants 0
5. if the number of participants increased, the probability would increase while if they decreased, the probability would decrease
What is Z-score?
The z score is a measure used in probability to determine the number of standard deviations the raw score is above or below the mean, it is given by the equation:
[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]
Given that:
the mean μ = 2.6 hours and a standard deviation(σ) of 0.3 hours.
[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]
1) What percent of the players finished the walk in less than 2 hours.
To calculate this, we use x as 2 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{2-2.6}{0.3}=-2[/tex]
From the normal probability distribution table, P(x < 2) = P(z < -2) = 0.0228 = 2.28%
2) What is the probability that two randomly chosen players completed the walk in 2.9 hours or more
To calculate this, we use x as 2.9 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{2.9-2.6}{0.3}=1[/tex]
From the normal probability distribution table, P(x > 2.9) = P(z > 1) = 1-P(z<1) = 1 - 0.8413 = 0.1587
3. What is the probability that four randomly chosen players completed the walk between 1.7 and 2.9 hours
To calculate this, we first use x as 1.7 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{1.7-2.6}{0.3}=-3[/tex]
For x as 2.9 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{2.9-2.6}{0.3}=1[/tex]
From the normal probability distribution table, P(1.7 < x < 2.9) = P(-3 < z < 1) = P(z<1) - P(z < -3) = 0.8413 - 0.0013 = 0.84
4. What observations can you make about the number of participants who complete the walk in more than 3.5 hours, given that there are 1,200 participants?
To calculate this, we use x as 3.5 hours, a number of samples (n) = 1200, and then find the z score.
[tex]Z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}=\dfrac{3.5-2.6}{\dfrac{0.3}{\sqrt{1200}}}=104[/tex]
From the normal probability distribution table, P(x > 3.5) = P(z > 104) = 1-P(z<104) = 1 - 1 = 0
5. What might you observe if the number of participants increased or decreased?
if the number of participants increased, the probability would increase while if they decreased, the probability would decrease
To know more about Z-scores follow
https://brainly.com/question/25638875
