(1 point) The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean $mu = 539$ and standard deviation $sigma = 26.2$. (a) What is the probability that a single student randomly chosen from all those taking the test scores 545 or higher? ANSWER: For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test. (b) What are the mean and standard deviation of the sample mean score $ar{x}$, of 35 students? The mean of the sampling distribution for $ar{x}$ is: The standard deviation of the sampling distribution for $ar{x}$ is: (c) What z-score corresponds to the mean score $ar{x}$ of 545? ANSWER: (d) What is the probability that the mean score $ar{x}$ of these students is 545 or higher? ANSWER: Note: You can earn partial credit on this problem.
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- The mean (μ) of the SAT scores is 539 and the standard deviation (σ) is 26.2. - We need to find the probability that a score (X) is 545 or more. First, calculate the Z-score for X = 545 using the formula: \[ Z = \frac{X - \mu}{\sigma} = \frac{545 - 539}{26.2} Show more…
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