Quantitative SAT Scores, Normal and Binomial The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100, and the scores are approximately Normally distributed. a. What is the probability that one randomly selected person will have an SAT score of 550 or more? b. What is the probability that four randomly selected people will all have SAT scores of 550 or more? c. For 800 randomly selected people, what is the probability that 250 or more will have scores of 550 or more? d. For 800 randomly selected people, on average how many should have scores of 550 or more? Round to the nearest whole number. e. Find the standard deviation for part d. Round to the nearest whole number. f. Report the range of people out of 800 who should have scores of 550 or more from two standard deviations below the mean to two standard deviations above the mean. Use your rounded answers to part d and e. g. If 400 out of 800 randomly selected people had scores of 550 or more, would you be surprised? Explain.
Quantitative SAT Scores, Normal and Binomial The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100, and the scores are approximately Normally distributed. a. What is the probability that one randomly selected person will have an SAT score of 550 or more? b. What is the probability that four randomly selected people will all have SAT scores of 550 or more? c. For 800 randomly selected people, what is the probability that 250 or more will have scores of 550 or more? d. For 800 randomly selected people, on average how many should have scores of 550 or more? Round to the nearest whole number. e. Find the standard deviation for part d. Round to the nearest whole number. f. Report the range of people out of 800 who should have scores of 550 or more from two standard deviations below the mean to two standard deviations above the mean. Use your rounded answers to part d and e. g. If 400 out of 800 randomly selected people had scores of 550 or more, would you be surprised? Explain.
Solution Summary: The author calculates the probability that a randomly selected person will have an SAT score of 550 or more.
The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100, and the scores are approximately Normally distributed.
a. What is the probability that one randomly selected person will have an SAT score of 550 or more?
b. What is the probability that four randomly selected people will all have SAT scores of 550 or more?
c. For 800 randomly selected people, what is the probability that 250 or more will have scores of 550 or more?
d. For 800 randomly selected people, on average how many should have scores of 550 or more? Round to the nearest whole number.
e. Find the standard deviation for part d. Round to the nearest whole number.
f. Report the range of people out of 800 who should have scores of 550 or more from two standard deviations below the mean to two standard deviations above the mean. Use your rounded answers to part d and e.
g. If 400 out of 800 randomly selected people had scores of 550 or more, would you be surprised? Explain.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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