Question 45: The distribution of scores of students heading to college in the math section of the SAT follows a normal d

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Question 45: The distribution of scores of students heading to college in the math section of the SAT follows a normal d

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Question 45: The distribution of scores of students heading to
college in the math section of the SAT follows a normal
distribution with mean πœ‡ = 520 and standard deviation 𝜎 = 115.
𝑋 = The score of a student heading to college in the math
section of the SAT
xΜ„ = The mean score of 100 students heading to college in the math
section of the SAT
βˆ‘ 𝑋 = The total score of 100 students heading to college in the
math section of the SAT (Please show all formulas, calculations and
the curves)
(a) What is the distribution of βˆ‘π‘‹?
(b) What is the probability that the total scores
of 100 students is more than 51500?
(c) What is the 65th percentile for the mean
scores of 100 students?
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