Sia
trevor685-68's Question
Math
Posted 8 months ago
Luke Andrew
Score Frequency Score Frequency
89 1 92 1
90 0 93 1
91 2 94 2
92 1 95 6
93 4 96 9
94 7 97 11
95 9 98 12
96 11 99 14
97 10 100 26
98 14 101 32
99 17 102 36
100 24 103 41
101 28 104 32
102 25 105 21
103 29 106 13
104 31 107 6
105 22 108 3
106 14 109 1
107 11 110 1
108 7 111 0
109 2 112 0
113 1
Total 269 269
a. Convert the frequency table to a Probability Distribution for both Luke and Andrew separately.
b. Which of the two has the highest probability of scoring less than 100. What is it?
c. Who is the better golfer – i.e. which of the two has the lowest average score (Expected Value). What are the two averages?
d. Who is the more consistent golfer – i.e. which of the two has the lowest standard deviation. What are the two standard deviations.
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Answer from Sia
Posted 8 months ago
Solution by Steps
step 1
To convert the frequency table to a probability distribution for Luke, divide each frequency by the total number of observations for Luke
step 2
The probability for each score is given by for Luke
step 3
Repeat the same process for Andrew to convert his frequency table to a probability distribution
Answer
Probability distributions for Luke and Andrew are calculated by dividing each score's frequency by the total frequency (269).
Key Concept
Probability Distribution
Explanation
A probability distribution assigns a probability to each outcome in the sample space of a random experiment.
step 4
To find who has the highest probability of scoring less than 100, sum the probabilities of scores less than 100 for both Luke and Andrew
step 5
The one with the higher sum of probabilities for scores less than 100 has the highest probability of scoring less than 100
Answer
The one with the higher sum of probabilities for scores less than 100 has the highest probability of scoring less than 100.
Key Concept
Cumulative Probability
Explanation
Cumulative probability is the sum of probabilities for all outcomes up to and including a certain event.
step 6
To determine the better golfer (lower average score), calculate the expected value for both Luke and Andrew
step 7
The expected value (average score) is calculated by summing the products of each score and its probability for both Luke and Andrew
Answer
The expected values (average scores) for Luke and Andrew are calculated by summing the products of each score and its probability.
Key Concept
Expected Value
Explanation
The expected value is the average of a probability distribution and represents the long-term average if the experiment were repeated many times.
step 8
To find who is the more consistent golfer (lowest standard deviation), calculate the standard deviation for both Luke and Andrew
step 9
The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences from the mean
Answer
The standard deviations for Luke and Andrew are calculated by taking the square root of the average of the squared differences from the mean.
Key Concept
Standard Deviation
Explanation
Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean.
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