Question

Scores on a recent national statistics exam were normally distributed with a mean of 82 and...

Scores on a recent national statistics exam were normally distributed with a mean of 82 and a standard deviation of 4.

  1. What is the probability that a randomly selected exam will have a score of at least 87?
  2. What percentage of exams will have scores between 80 and 85?
  3. If the top 3% of test scores receive merit awards, what is the lowest score eligible for an award?

Homework Answers

Answer #1

Given that, mean = 82

stsndard deviation = 4

i) We want to find, P(X >= 87)

Therefore, required probability is 0.1056

ii) We want to find, P(80 < X < 85)

Therefore, required probability is 0.4649

iii) We want to find, the value of x such that, P(X > x) = 0.03

Therefore, lowest score eligible for an award is 89.52

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Scores on exam 2 for statistics are normally distributed with mean 70 and standard deviation 15....
Scores on exam 2 for statistics are normally distributed with mean 70 and standard deviation 15. a. Find a, if P(x>a)= 0.9595 b.What is the probability that a randomly selected score is above 65?
Assume that statistics scores that are normally distributed with a mean 75 and a standard deviation...
Assume that statistics scores that are normally distributed with a mean 75 and a standard deviation of 4.8 (a) Find the probability that a randomly selected student has a score greater than 72. (b) Find the probability that a randomly selected student has a score between 70 and 80. (c) Find the statistics score separating the bottom 99.5% from the top 0.5%. (d) Find the statistics score separating the top 64.8% from the others.
The scores for the final exam in a particular class are approximately normally distributed with a...
The scores for the final exam in a particular class are approximately normally distributed with a meann of 78.4 points and standard deviation of 5.7. A. What score would a student nneed to score inn the top 20% of sudent scores? Round two decimal places. B. What is the probablity that a randomly selected group of 36 students will have a eman score of more than 80 points? Innclude a probability statement. Round four decimal places.
The final exam scores in a statistics class were normally distributed with a mean of 70...
The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored more than 75% on the exam?
Suppose that your statistics professor tells you that the scores on a midterm exam were approximately...
Suppose that your statistics professor tells you that the scores on a midterm exam were approximately normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all scores have been designated A’s. What is the minimum score that you must earn in order to receive a letter grade A.
A math professor notices that scores from a recent exam are normally distributed with a mean...
A math professor notices that scores from a recent exam are normally distributed with a mean of 72 and a standard deviation of 5. (a) What score do 75% of the students exam scores fall below? Answer: (b) Suppose the professor decides to grade on a curve. If the professor wants 2.5% of the students to get an A, what is the minimum score for an A? Answer:
Suppose the scores on a statistic exam are normally distributed with a mean of 77 and...
Suppose the scores on a statistic exam are normally distributed with a mean of 77 and a variance of 25. A. What is the 25th percentile of the scores? B. What is the percentile of someone who got a score of 62? C. What proportion of the scores are between 80 and 90? D. Suppose you select 35 tests at random, what is the proportion of scores above 85?
The scores on a psychology exam were normally distributed with a mean of 58 and a...
The scores on a psychology exam were normally distributed with a mean of 58 and a standard deviation of 9. What is the standard score for an exam score of 57​? The standard score is ______
Exam scores in a MATH 1030 class is approximately normally distributed with mean 87 and standard...
Exam scores in a MATH 1030 class is approximately normally distributed with mean 87 and standard deviation 5.2. Round answers to the nearest tenth of a percent. a) What percentage of scores will be less than 93? % b) What percentage of scores will be more than 80? % c) What percentage of scores will be between 79 and 88? %
A math professor notices that scores from a recent exam are Normally distributed with a mean...
A math professor notices that scores from a recent exam are Normally distributed with a mean of 72 and a standard deviation of 8. Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?