Question

10. The grade distribution of a Basic English course in a high school (total 3500 students)...

10. The grade distribution of a Basic English course in a high school (total 3500 students) is normally distributed with its mean, 3.2 and standard deviation, 0.61. 1) If a student is randomly selected, find the probability that the student’s score is higher than 3.0?2) If you collect a sample of 30 students, what is the probability that the sample mean is less than 3.0?

Homework Answers

Answer #1

Solution :

1)

P(x > 3.0) = 1 - P(x < 3.0)

= 1 - P[(x - ) / < (3.0 - 3.2) / 0.61)

= 1 - P(z < -0.3279)

= 1 - 0.3715

= 0.6285

Probability = 0.6285

2)

= / n = 0.61/ 30 = 0.1114

P( < 3.0) = P(( - ) / < (3.0 - 3.2) / 0.1114)

= P(z < -1.7953)

= 0.0363

Probability = 0.0363

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
In a recent year, grade 6 Michigan State public school students taking a mathematics assessment test...
In a recent year, grade 6 Michigan State public school students taking a mathematics assessment test had a mean score of 303.1 with a standard deviation of 36. Possible test scores could range from 0 to 1000. Assume that the scores were normally distributed. a. Find the probability that a student had a score higher than 295. b. Find the probability that a student had a score between 230 and 305. c. What is the highest score that would still...
In a recent​ year, scores on a standardized test for high school students with a 3.50...
In a recent​ year, scores on a standardized test for high school students with a 3.50 to 4.00 grade point average were normally​ distributed, with a mean of 38.238.2 and a standard deviation of 2.22.2. A student with a 3.50 to 4.00 grade point average who took the standardized test is randomly selected. ​(a) Find the probability that the​ student's test score is less than 3737. The probability of a student scoring less than 3737 is 0.29120.2912. ​(Round to four...
In a recent year, the ACT scores for the English portion of the test were normally...
In a recent year, the ACT scores for the English portion of the test were normally distributed, with a mean of 20 and a standard deviation of six. A high school student who took the English portion of the ACT is randomly selected a) Find the probability that the student’s ACT score is less than15? b) Find the probability that the student’s ACT score is between 18 and25? c) Find the probability that the student’s ACT score is more than34?...
In a recent year, grade 8 Washington State public schools students taking a mathematics assessment test...
In a recent year, grade 8 Washington State public schools students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. a) What is the lowest score that still place a student in the top 15% of the scores? b) Find the probability that a student had a score higher than 350. c) Find the probability that...
The scores of students on the SAT college entrance examinations at a certain high school had...
The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=539.3 and standard deviation σ=29.9. (a) What is the probability that a single student randomly chosen from all those taking the test scores 543 or higher? ANSWER:   For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test. (b) What are the mean and standard deviation of the sample mean score x¯,...
Let X be the score on a national test of randomly selected student from West High...
Let X be the score on a national test of randomly selected student from West High School and Y be the score on the same test of a randomly selected student from East High School. Suppose X has a normal distribution with mean 50 and variance 29. Y has a normal distribution with mean 47 and variance 35, and X and Y are independent. If a student from each high school is randomly selected, what is the probability that the...
) The mean ACT mathematics score for 60 randomly selected high school students is 20.6. Assume...
) The mean ACT mathematics score for 60 randomly selected high school students is 20.6. Assume the population standard deviation is 5.4. The mean ACT science score for 75 other randomly selected high school students is 20.8. Assume the population standard deviation is 5.6. At ? = 0.01, can you reject the claim that the ACT math and ACT science scores are equal? a.) Verify that 1.) Both population standard deviations are known. _____ 2.) The samples taken are random....
6.18 ACT scores of high school seniors. The scores of your state’s high school seniors on...
6.18 ACT scores of high school seniors. The scores of your state’s high school seniors on the ACT college entrance examination in a recent year had mean m 5 22.3 and standard deviation s 5 6.2. The distribution of scores is only roughly Normal. (a) What is the approximate probability that a single student randomly chosen from all those taking the test scores 27 or higher?(b) Now consider an SRS of 16 students who took the test. What are the...
1.The combined SAT scores for the students at a local high school are normally distributed with...
1.The combined SAT scores for the students at a local high school are normally distributed with a mean of 1493 and a standard deviation of 307. The local college includes a minimum score of 1278 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement? P(X > 1278) = % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). 2.A distribution of values is...
The scores of fourth grade students on a mathematics achievement test follow a normal distribution with...
The scores of fourth grade students on a mathematics achievement test follow a normal distribution with a mean of 75 and standard deviation of 4. What is the probability the sample mean score of 64 randomly selected students is between 74 and 76?