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In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken?
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In a certain junior olympics javelin throw distanes are well aproximat...
**Probability of being disqualified in the first round:**
To find the probability of being disqualified in the first round, we need to calculate the area under the Gaussian curve to the left of 27m. This represents the probability that a throw falls below 27m.
1. Calculate the z-score:
The z-score represents the number of standard deviations a data point is from the mean. It is calculated using the formula:
z = (x - μ) / σ
where x is the value (27m), μ is the mean (30m), and σ is the standard deviation (5m).
z = (27 - 30) / 5
z = -0.6
2. Lookup the z-score in the standard normal distribution table:
The standard normal distribution table provides the area under the curve to the left of a given z-score. In this case, we need to find the area to the left of -0.6.
Looking up the z-score in the table, we find that the area to the left of -0.6 is approximately 0.2743.
3. Calculate the probability of being disqualified:
The probability of being disqualified in the first round is equal to the area under the curve to the left of 27m, which is the same as the area to the left of -0.6.
P(disqualified) = 0.2743
Therefore, the probability of being disqualified in the first round is approximately 0.2743, or 27.43%.
**Probability of the record being broken in the main event:**
To find the probability that the record will be broken in the main event, we need to calculate the area under the Gaussian curve to the right of 44m. This represents the probability that a throw exceeds 44m.
1. Calculate the z-score:
The z-score is calculated using the same formula as before:
z = (x - μ) / σ
where x is the value (44m), μ is the mean (30m), and σ is the standard deviation (5m).
z = (44 - 30) / 5
z = 2.8
2. Lookup the z-score in the standard normal distribution table:
This time, we need to find the area to the right of 2.8.
Looking up the z-score in the table, we find that the area to the right of 2.8 is approximately 0.0026.
3. Calculate the probability of the record being broken:
The probability of the record being broken in the main event is equal to the area under the curve to the right of 44m, which is the same as the area to the right of 2.8.
P(record broken) = 0.0026
Therefore, the probability that the record will be broken in the main event is approximately 0.0026, or 0.26%.
To find the probability of being disqualified in the first round, we need to calculate the area under the Gaussian curve to the left of 27m. This represents the probability that a throw falls below 27m.
1. Calculate the z-score:
The z-score represents the number of standard deviations a data point is from the mean. It is calculated using the formula:
z = (x - μ) / σ
where x is the value (27m), μ is the mean (30m), and σ is the standard deviation (5m).
z = (27 - 30) / 5
z = -0.6
2. Lookup the z-score in the standard normal distribution table:
The standard normal distribution table provides the area under the curve to the left of a given z-score. In this case, we need to find the area to the left of -0.6.
Looking up the z-score in the table, we find that the area to the left of -0.6 is approximately 0.2743.
3. Calculate the probability of being disqualified:
The probability of being disqualified in the first round is equal to the area under the curve to the left of 27m, which is the same as the area to the left of -0.6.
P(disqualified) = 0.2743
Therefore, the probability of being disqualified in the first round is approximately 0.2743, or 27.43%.
**Probability of the record being broken in the main event:**
To find the probability that the record will be broken in the main event, we need to calculate the area under the Gaussian curve to the right of 44m. This represents the probability that a throw exceeds 44m.
1. Calculate the z-score:
The z-score is calculated using the same formula as before:
z = (x - μ) / σ
where x is the value (44m), μ is the mean (30m), and σ is the standard deviation (5m).
z = (44 - 30) / 5
z = 2.8
2. Lookup the z-score in the standard normal distribution table:
This time, we need to find the area to the right of 2.8.
Looking up the z-score in the table, we find that the area to the right of 2.8 is approximately 0.0026.
3. Calculate the probability of the record being broken:
The probability of the record being broken in the main event is equal to the area under the curve to the right of 44m, which is the same as the area to the right of 2.8.
P(record broken) = 0.0026
Therefore, the probability that the record will be broken in the main event is approximately 0.0026, or 0.26%.
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In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken?
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In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken?.
In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain junior olympics javelin throw distanes are well aproximated by a gaussion distribution for which mean is 30m and standard deviation is 5m.in a qualifying round contestants must throw farther than 27m to qualify.in the main event the record throw is 44m. 1.what is the probability of being disqualify in the first round. 2.in the main event what is the probability that the record will be broken?.
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