The composite ACT scores for Idaho students who took the test in 2019 have average 22.3 with the standard deviation 2.25 and approximately normal distributed. In a random sample of 49 students who took the exam in 2019, the average composite ACT score is 23.5 with standard deviation 1.06. (show your work)Which one is true?3 and 2.25 are statistics, and 1.06 are parameters.3 and 2.25 are parameters, and 1.06 are statistics.All numbers 22.3, 2.25 and 23.5, 1.06 are parameters.All numbers 22.3, 2.25 and 23.5, 1.06 are statistics.What is the probability that the score is 23 or more if we random select one student?Find the 85th percentile the composite ACT scores for Idaho students

Let X denotes the test scores. Then given: μx = 22.3 & σx=2.25 Sample size, n = 49 Sample mean, x¯=23.5 Sample SD, s = 1.06 Part 1: From the given information 22.3 and 2.25 are parameters, and 23.5 & 1.06 are statistics. Part 2: The required probability is P(X≥23)=PX-μxσx≥23-μxσx = PZ≥23-22.32.25 = P(Z≥0.31) = 1 - P(Z≤0.31) = 1 - 0.6217 = 0.3783 Part c: Let x be the 85th percentile then P(X≤x) = 0.85⇒PX-μxσx≤x-μxσx =0.85⇒P(Z≤z) = 0.85 then from the normal probability tables (below), we have z = 1.04 ⇒x-22.32.25= 1.04⇒ x = 24.64

Answered: The composite ACT scores for Idaho…

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The composite ACT scores for Idaho students who took the test in 2019 have average 22.3 with the standard deviation 2.25 and approximately normal distributed. In a random sample of 49 students who took the exam in 2019, the average composite ACT score is 23.5 with standard deviation 1.06. (show your work)

Which one is true?

3 and 2.25 are statistics, and 1.06 are parameters.
3 and 2.25 are parameters, and 1.06 are statistics.
All numbers 22.3, 2.25 and 23.5, 1.06 are parameters.
All numbers 22.3, 2.25 and 23.5, 1.06 are statistics.

What is the probability that the score is 23 or more if we random select one student?

Find the 85^th percentile the composite ACT scores for Idaho students

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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