Question

In 2016 the US Scholastic Assessment Test (SAT) which is used to assess students’ performance for admissions to US universities was completely revised. In 2017 across the entire US the average SAT score was 1060 with a standard deviation of 195 (these can be taken as population values) a. What is the probability any one student taking the SAT scores more than 1500 on the test? What assumption would you have to make to do this calculation? b. Suppose a university randomly sampled 100 students to calculate their average score. Describe the sampling distribution of the sample mean. c. What is the probability that a sample of 100 students had an average score of more than 1100?

          In 2016 the US Scholastic Assessment Test (SAT) which is used to assess students’ performance for admissions to US universities was completely revised. In 2017 across the entire US the average SAT score was 1060 with a standard deviation of 195 (these can be taken as population values)
a. What is the probability any one student taking the SAT scores more than 1500 on the test? What assumption would you have to make to do this calculation?
b. Suppose a university randomly sampled 100 students to calculate their average score. Describe the sampling distribution of the sample mean.
c. What is the probability that a sample of 100 students had an average score of more than 1100?
        
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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In 2016 the US Scholastic Assessment Test (SAT) which is used to assess students’ performance for admissions to US universities was completely revised. In 2017 across the entire US the average SAT score was 1060 with a standard deviation of 195 (these can be taken as population values) a. What is the probability any one student taking the SAT scores more than 1500 on the test? What assumption would you have to make to do this calculation? b. Suppose a university randomly sampled 100 students to calculate their average score. Describe the sampling distribution of the sample mean. c. What is the probability that a sample of 100 students had an average score of more than 1100?
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Transcript

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00:01 So, to solve this problem, we will use the formula to find the z value and hence the probability from that.
00:07 So, this will be the value x minus mu divided by standard deviation divided by square root of n.
00:14 Now, x will be the value of interest for us and mu is the population mean, sigma is the population standard deviation.
00:23 So, this is 100 and n is 90.
00:27 Now, for the first one for evidence based reading and writing, we have to do it within 10 points of the mean.
00:37 So, the mean for evidence based writing in this is 533.
00:43 So, x values basically we need to find the values of x between 543 and 523.
00:51 So, this will be equal to probability of x is equal to 543 less than or equal to 543 minus probability of x less than or equal to 523, ok.
01:09 So, for both of this we will find the z value.
01:12 So, z will be equal to 543 minus 533 divided by 100 divided by square root of 90...
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