Solution :
Let X represents the composite ACT scores.
Given that, X ~ N(21.0, 5.4²)
μ = 21.0 and σ = 5.4
To qualify for the University of Georgia, one's ACT score must be in top 7%. Hence, the minimum ACT score will be the corresponding to 93th percentile.
Let the minimum ACT score needed is k.
Hence, P(X < k) = 0.93
We know that if X ~ N(μ, σ²) then,
Using "qnorm" function of R we get, P(Z < 1.476) = 0.93
Comparing, P(Z < 1.476) = 0.93 and (1) we get,
Hence, the needed ACT score is 29.
Please rate the answer. Thank you.
Question 21 (2.34375 points) The mean composite ACT score for graduating seniors between 2013 and 2015...
Question 17 (2.34375 points) The mean composite ACT score for graduating seniors between 2013 and 2015 was 21.0 with a standard deviation of 5.4. Assume the composite ACT scores are normally distributed. What is the probability that a randomly selected composite ACT score is between 19 and 23? Round answer to four decimal places.
Suppose ACT Composite scores are normally distributed with a mean of 20.6 and a standard deviation of 5.2. A university plans to admit students whose scores are in the top 40%. What is the minimum score required for admission? Round your answer to the nearest tenth, if necessary.
Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 9 % . what is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.
suppose ACT reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9 . A university plans to award scholarships to students who’s scores are in the top 9%. what is the minimum score required for the scholarship? Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 9 %. What is the...
Step By Step 4 of 5 Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 9 % . What is the minimum score required for the scholarship? TablesKeypad we have found the value-z =-1.34, such that the area to the left of-z is approximately 0.09. Since the standard normal curve is symmetric and centered at zero, the...
It is reported that the ACT scores of freshman students at NMSU is approximately Normally distributed, with mean of 20.5 and standard deviation of 5.1. (1) (3pts) If the university decides to offer a scholarship to the top 2% of students, how high does a student need to score on ACT test to qualify for that scholarship? (No points will be given without proper steps) (2) (3pts) A math class has 20 freshmen enrolled. If we assume the 20 freshmen...
please help thank you in advance It is reported that the ACT scores of freshman students at NMSU is approximately Normally distributed, with mean of 21.1 and standard deviation of 4.5. (1) (3pts) If the university decides to offer a scholarship to the top 3% of students, how high does a student need to score on ACT test to qualify for that scholarship? (No points will be given without proper steps) (2)(3pts) A math class has 30 freshmen enrolled. If...
Suppose that composite scores on the ACT test for the school graduating class in a certain year had a mean of 24.2 and a standard deviation of 4.6. In all, 1,823,241 students in this class took the test, and of these, 6,947 had scores higher than 36.4 and 2,404 had scores exactly 36.4. ACT scores are always whole numbers, but the Normal N(24.2, 4.6) distribution can include any value, not just whole numbers. What is more, there is no area...
To qualify for a scholarship, applicants must score in the top 4% on a standardized test. If the test scores are normal with a mean of 500 and a standard deviation of 30. What minimum exam score is needed to qualify?
Suppose that composite scores on the ACT test for the school graduating class in a certain year had a mean of 24.2 and a standard deviation of 4.6. In all, 1,823,241 students in this class took the test, and of these, 6,947 had scores higher than 36.4 and 2,404 had scores exactly 36.4. ACT scores are always whole numbers, but the Normal N(24.2, 4.6) distribution can include any value, not just whole numbers. What is more, there is no area...