On a nationwide test taken by high school students, the mean score was 49 and the standard deviation was 12. The scores were normally distributed. Complete the following statements.(a) Approximately 95% of the students scored between and .(b) Approximately of the students scored between 13 and 85.
Question
On a nationwide test taken by high school students, the mean score was 49 and the standard deviation was 12. The scores were normally distributed. Complete the following statements.(a) Approximately 95% of the students scored between and .(b) Approximately of the students scored between 13 and 85.
Solution
(a) The 95% of the students scored between (mean - 2standard deviation) and (mean + 2standard deviation). So, 95% of the students scored between (49 - 212) and (49 + 212), which is between 25 and 73.
(b) To find the percentage of students who scored between 13 and 85, we need to calculate the z-scores for these values and look up the corresponding percentages in a standard normal distribution table.
The z-score is calculated as (X - mean) / standard deviation.
For X = 13, the z-score is (13 - 49) / 12 = -3. For X = 85, the z-score is (85 - 49) / 12 = 3.
Looking up these z-scores in a standard normal distribution table, we find that the percentage of students who scored less than 13 is approximately 0.1% and the percentage of students who scored less than 85 is approximately 99.9%.
Therefore, approximately 99.8% (99.9% - 0.1%) of the students scored between 13 and 85.
Similar Questions
In a Statistics test, the average mark is 82 and the standard deviation is 5. All the students from 88 marks up to 94 marks will receive a B grade. If the marks have a normal distribution and 8 students receive B grade, determine the total number of students who sat for the test.
A standardized test has a mean score of 500 points with a standard deviation of 100 points. Five students' scores are shown below.Adam: 575 Beth: 690 Carlos:750 Doug:280 Ella: 440Which of the students have scores within two standard deviations of the mean?Group of answer choicesCarlos, DougAdam, Beth, Carlos, EllaAdam, BethAdam, Beth, Ella
Question 4Your instructor tells you that the recent exam had a mean of 80 points and a standard deviation of 2.3. Interpret the standard deviation value in everyday language.1 pointThe maximum score was 82.3.Most students earned an 80 on the exam.The typical score was 2.3 points away from the mean.The range of scores was 4.6.
A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 208 graduating seniors and found the mean score to be 525 with a standard deviation of 115. At the 95% confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest tenth.
The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with a mean of μ = 18.6 and a standard deviation of σ = 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as the scores in the population.What is the standard deviation of the sampling distribution of the sample mean for a random sample of 36 students
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.