Question

In: Math

The grades of a group of 1000 students in an exam are normally distributed with a...

The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation of 10. A student is randomly selected from the group. Find the probability that;

a. Their grade is greater than 80

b. Their grade is less than 50

c. That their grade is between 50 and 80

d. Approximately, how many students have grade greater than 80% and how many have less than 50%

Solutions

Expert Solution


Related Solutions

A set of final exam grades in ST2500 course is normally distributed with mean 70 and...
A set of final exam grades in ST2500 course is normally distributed with mean 70 and standard deviation of 8. (a) What is the probability of getting a grade of A(greater or equal 80) on this exam? (4) (b) What is the probability of that a student scored between 65 and 79? (4) (c) The probability is 10% that a student taking the exam scores higher than what grade?
Exam grades: Scores on a statistics final in a large class were normally distributed with a...
Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 70 and a standard deviation of 10. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 42nd percentile of the scores. (b) Find the 71st percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 10% of the class. What...
Suppose the scores of students on an exam are normally distributed with a mean of 340...
Suppose the scores of students on an exam are normally distributed with a mean of 340 and a standard deviation of 57. Then according to the Empirical Rule approximately 99.7 of the exam scores lie between the integers    and    .
A group of 1000 students wrote an entrance exam for the University of Statistics. The mean...
A group of 1000 students wrote an entrance exam for the University of Statistics. The mean score was 62 with a standard deviation of 12. Assuming a Normal Distribution, answer the following questions: What is the probability of a student scoring above 75? What is the probability of a student failing? (i.e. below 50) How many students failed? What is the minimum mark you would need to score to be in the top 10%? What is the minimum mark you...
Exam grades across all sections of introductory statistics at a large university are approximately normally distributed...
Exam grades across all sections of introductory statistics at a large university are approximately normally distributed with a mean of 72 and a standard deviation of 11. Use the normal distribution to answer the following questions. (a) What percent of students scored above an 88 ?Round your answer to one decimal place. (b) What percent of students scored below a 59 ?Round your answer to one decimal place. (c) If the lowest 7%of students will be required to attend peer...
The SAT scores for students are normally distributed with a mean of 1000 and a standard...
The SAT scores for students are normally distributed with a mean of 1000 and a standard deviation of 200. What is the probability that a sample of 45 students will have an average score between 970 and 1010? Round your answer to 3 decimal places.
The heights of 1000 students are approximately normally distributed with a mean of 174.5centimeters and a...
The heights of 1000 students are approximately normally distributed with a mean of 174.5centimeters and a standard deviation of 6.9 centimeters. Suppose 200 random samples ofsize 25 are drawn from this population and the means recorded to the nearest tenth of acentimeter. Determine (a) the mean and standard deviation of the sampling distribution of ̄X; (b) the number of sample means that fall between 171 and 177 cm . Let X be a random variable following a continuous uniform distribution...
The heights of 1000 students are normally distributed with a mean of 177.5 centimeters and a...
The heights of 1000 students are normally distributed with a mean of 177.5 centimeters and a standard deviation of 6.7 centimeters. Assuming that the heights are recorded to the nearest​ half-centimeter, how many of these students would be expected to have heights ​(a) less than 167.0 centimeters? ​(b) between 173.5 and 185.0 centimeters​ inclusive? ​(c) equal to 180.0 ​centimeters? ​(d) greater than or equal to 191.0 ​centimeters?
The SAT scores for students are normally distributed with a mean of 1000 and a standard...
The SAT scores for students are normally distributed with a mean of 1000 and a standard deviation of 200. What is the probability that a sample of 36 students will have an average score between 970 and 1010? Round your answer to 3 decimal places.
There are 300 students enrolled in Business Statistics. Historically, exam scores are normally distributed with a...
There are 300 students enrolled in Business Statistics. Historically, exam scores are normally distributed with a standard deviation of 26.7. Your instructor randomly selected a sample of 40 examinations and finds a mean of 64.2. Determine a 90% confidence interval for the mean score for all students taking the course. 90% CI = to
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT