Question

In: Statistics and Probability

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.

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 1000

standard deviation = = 200

n = 45

= 1000

=  / n= 200/ 45=29.81

P(970<     < 1010) = P[(970-1000) / 29.81< ( - ) /   < (1010-1000) / 29.81)]

= P( -1.01< Z <0.34 )

= P(Z < 0.34) - P(Z <-1.01 )

Using z table

=0.6331-0.1562

=0.4769

probability=0.477

orchestra answered 2 years ago
Next > < Previous

Related Solutions

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.
Assume that SAT scores are normally distributed with a mean of 1000 and a standard deviation...
Assume that SAT scores are normally distributed with a mean of 1000 and a standard deviation of 150. Use this information to answer the following questions. Round final answers to the nearest whole number. What is the lowest SAT score that can be in the top 10% of testers? What is the highest SAT score that can be in the bottom 5% of testers? Between which two SAT scores do the middle 50% of testers lie?
3)   Scores on the SAT are normally distributed with a mean of 500 and a standard...
3)   Scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100 What is the probability of obtaining a score greater than 640? What is the probability of obtaining a score less than 390? What is the probability of obtaining a score between 725 and 800? What is the probability of obtaining a score either less than 375 or greater than 650? 4) If you obtained a score of 75 on an test,...
SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of...
SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). If a sample of 35 students are selected randomly, find the probability that the sample mean is above 470. A.) 0.244 B.) 0.9756 C.) 0.0445 D.) 0.0244
Suppose that SAT math scores are normally distributed with a mean of 516 and a standard...
Suppose that SAT math scores are normally distributed with a mean of 516 and a standard deviation of 115, while ACT math scores have a normal distribution with a mean of 22 and a standard deviation of 5. James scored 650 on the SAT math and Jacob scored 29 on the ACT math. Who did better in terms of the standardized z-score? Group of answer choices James Jacob They did relatively the same. Impossible to tell because of the scaling
SAT scores normal distributed mean 985 and standard deviation of 169. AMT scores are normally distributed...
SAT scores normal distributed mean 985 and standard deviation of 169. AMT scores are normally distributed with a mean of 24.6 and a standard deviation of 3.5. It is assumed that the two tests measure thw same aptitude bit use different scales. a). if a student is 46-percentile in SAT, find the actual SAT score. b). what would be the equivalent AMT score? c). if a student gets SAT score of 1220, find the equivalent AMT score.
The SAT scores for US high school students are normally distributed with a mean of 1500...
The SAT scores for US high school students are normally distributed with a mean of 1500 and a standard deviation of 100. 1. Calculate the probability that a randomly selected student has a SAT score greater than 1650. 2. Calculate the probability that a randomly selected student has a SAT score between 1400 and 1650, inclusive. 3. If we have random sample of 100 students, find the probability that the mean scores between 1485 and 1510, inclusive.
1. SAT math scores are normally distributed with a mean 525 and a standard deviation of...
1. SAT math scores are normally distributed with a mean 525 and a standard deviation of 102. In order to qualify for a college you are interested in attending your SAT math score must be in the highest 9.34% of all SAT scores. What is the minimum score you need on the SAT to qualify for the college? 2. If you get into this college you are interested in running for the track team. To qualify for the track team...
Math SAT scores are known to be normally distributed with mean of 500 and standard deviation...
Math SAT scores are known to be normally distributed with mean of 500 and standard deviation of 100. Answer the following questions. (I also want to see good notation and some of your calculations.) a) Suppose we randomly select one person who has taken the SAT. What is the probability their math score is between 525 and 550? b) Suppose we randomly select 25 people who have taken the SAT. What is the probability their average math score is between...
Math SAT scores (Y) are normally distributed with a mean of 1500 and a standard deviation...
Math SAT scores (Y) are normally distributed with a mean of 1500 and a standard deviation of 140. An evening school advertises that it can improve students' scores by roughly a third of a standard deviation, or 30 points, if they attend a course which runs over several weeks. (A similar claim is made for attending a verbal SAT course.) The statistician for a consumer protection agency suspects that the courses are not effective. She views the situation as follows:...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT