1.Suppose that a scholarship qualifying exam is given to a large number of students every year.
Over the last 5 years, the exam results are normally distributed with a mean of 35 and a standard deviation of 7.
Suppose over that period of time 10000 students took the test
If you and received a 56, how many students (approximately) did better than you? What does that say about your score?
What if your friend received a 28? How many students approximately) had a lower score than youir friend?
Make use of the empirical rule to explain your conclusion. You should not have to do any computations with Stat Crunch or the Tables to answer this question. The Emprical rule and some knowledge about the shape of th normal distribution is all tha you need.
If the scholarship is awarded to 2.5% of the students who take the exam, aproximatly what would be the minimum score that would be needed to qualify?
2.Suppose you hear that a family has two children, but you do not know the gender of either child. What is the probability that they have a boy and a girl? Does it change your calculation of the probability if you are told the additional information that theolderchild is a boy? Does it change your calculation if you are told that one of the children is named Charles? (Charles is a boy, but we don't know if Charles is older or younger than his sibling). Explain, in terms of probability theory, how you reached your conclusions. The concept of the Sample Space will be key to understanding the solution. (For the purposes of this question assume that a child is equally likely to be a boy or a girl and that the genders of children in the same family are independent of each other.)
3.Consider the repair costs for two brands of automobiles, which we shall call Brand A and Brand B. You are given a data set that contains information concerning the repair costs of the two brands. You discover that the values are distributed approximately as a normal distribution. The mean repair cost for each is $500 per year. The standard deviation of the repair costs for Brand A is $100.00 and the standard deviation of the repair costs for brand B is $75.00. Given this information, can you find the following information.
1. What is the repair cost that represents the 90th percentile of annual repair costs associated with Brand A cars? Expalin how you determined this.
2. What percentage of Brand B cars will cost more than $600.00 per year to repair? Explain how you determined this.
3. Determine what percentage of cars in the sample will have annual repair costs between $450.00 and $575.00 for each of the two brands. There are a couple of ways of getting the answer for this - neither one of the needs to require the use of tables.
4. Based on the information given about these two vehicles, which would you prefer to purchase if all other factors were equal. Why do say this. Make sure your reasoning is statistical and based only on the statistics you have been given.
4.The SAT Test and ACT Test are two commonly used test used for college admissions.
Each part of the SAT Test is constructed so that the historical mean of all of the scores is 500 and the standard deviation is 100.
Each part of the ACT Test is designed to have a mean of 18 and the standard deviation is 6.
Suppose that a high school student applying for college admissions gets a score of 630 on the Math SAT and a score of 27 on the Math part of the ACT. On which test did the student have a better performance? Explain how you made that determination.
Another student earned a score of 750 on the English part of the SAT. What score would they have to get on the English part of the ACT to demonstrate the same level of performance?Explain how you made that determination. You should be able to use the Stat Crunch Calculator to help make these calculations a lot easier.