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1) If SAT scores are normally distributed with a mean of 1,000
and a standard deviation of 200, what is the probability of a
student scoring 1,100 or higher on the SAT?
2) For this hypothetical SAT distribution, what is the
probability of a student scoring 910 or lower on the SAT?
3) For this hypothetical SAT distribution, what is the
probability of a student scoring 910 or lower or 1,100 or
higher?
4) For this hypothetical SAT distribution, what is the
probability of selecting a student who scored 910 or lower followed
by a student who scored 1,100 or higher on the SAT?
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08:43
The distribution of scores on the SAT is approximately normal with a mean of $\mu=500$ and a standard deviation of $\sigma=100 .$ For the population of students who have taken the SAT:a. What proportion have SAT scores less than $400 ?$b. What proportion have SAT scores greater than $650 ?$c. What is the minimum SAT score needed to be in the highest $20 \%$ of the population?d. If the state college only accepts students from the top $40 \%$ of the SAT distribution, what is the minimum SAT score needed to be accepted?
04:35
The national average SAT score (for Verbal and Math) is 1028 . If we assume a normal distribution with $\sigma=92,$ what is the 90th percentile score? What is the probability that a randomly selected score exceeds $1200 ?$
08:15
The number of students taking the SAT has risen to an all-time high of more than 1.5 million (College Board, August $26,2008 ) .$ Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows.a. Let $x$ be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable.b. What is the probability that a student takes the SAT more than one time?c. What is the probability that a student takes the SAT three or more times?d. What is the expected value of the number of times the SAT is taken? What is your interpretation of the expected value?e. What is the variance and standard deviation for the number of times the SAT is taken?
07:38
The national average for the math portion of the College Board’s SAT is 515 (The WorldAlmanac, 2009 ). The College Board periodically rescales the test scores such that thestandard deviation is approximately $100 .$ Answer the following questions using a bell-shaped distribution and the empirical rule for the verbal test scores.a. What percentage of students have an SAT math score greater than 615$?$b. What percentage of students have an SAT math score greater than 715$?$c. What percentage of students have an SAT math score between 415 and 515$?$d. What percentage of students have an SAT math score between 315 and 615$?$
07:10
Transcript
So you have been to let’s let’s go represented by So S. A. T scores present X. To our exes not only distributed with me, 1000 invariance to be 200 squared. So this implies that Austen a division is 200. So I was there because X -1000 over 200. The standard normal distribution. So for the first but we have to find probability of X. We didn’t not equal to 1100 which is 1100. So we get probability of x minus 10,000. Okay 3000 Over 200. Yes. We didn’t know you go to 1,100 -1000 over 200. So we get probability upset greater than or equal to zero points. Right? So we get 1- the probability of Less than 2.5 kids. 1 -0.6914 six. From the standard normal distribution table That’s not really noticeable. So this gives us 0.30854. Is that required probability. So when it comes to the second part we have to find the probability of x less or equal to 910. So this gives us a…
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