Question

2. Problem 2 is adapted from the Problem 39 at the end of Chapter 11. Please solve this problem in Excel and submit your Excel spreadsheet. The problem is as follows: The state of Virginia has implemented a Standard of Learning (SOL) test that all public school students must pass before they can graduate from high school. A passing grade is 75. Montgomery County High School administrators want to gauge how well their students might do on the SOL test, but they don't want to take the time to test the whole student population. Instead, they selected 20 students at random and gave them the test. The results are as follows: 83 79 56 93 48 92 37 45 72 71 92 71 66 83 81 80 58 95 67 78 Assume that SOL test scores are normally distributed. a. Compute the mean and standard deviation for these data. b. Determine the probability that a student at the high school will pass the test. c. How many percent of students will receive a score between 75 and 95? d. What score will put a student in the bottom 15% in SOL score among all students who take the test? e. What score will put a student in the top 2% in SOL score among all students who take the test? 3. The average male drinks 2 L of water when active outdoors (with a standard deviation of 0.8L). You are planning a full day nature trip for 100 men and will bring 210 L of water. What is the probability that you will run out? Please solve this problem in Excel and submit your Excel file.

Answer 1

2) Let X be the SOL test score of a student at the high school. X is normally distributed.

a)

be the sample mean and sample standard deviations of SOL test scores at the high school.  

We will estimate the population mean  SOL test scores at the high school using the sample mean as

We will estimate the population standard deviation of scores as

b. Determine the probability that a student at the high school will pass the test is same as the probability that a student at the high school scores 75 or more

P(X>=75)

c. How many percent of students will receive a score between 75 and 95?

P(75<X<95)

d. What score will put a student in the bottom 15% in SOL score among all students who take the test?

Let q be the score that will put a student is the bottom 15%

P(X<q)=0.15

e. What score will put a student in the top 2% in SOL score among all students who take the test?

Let r be the score that will put a student in the top 2%

P(X>r) = 0.02 or P(X<r)=1-0.02=0.98

Prepare the following sheet

get this

3) Let X be the amount of water any given male drinks, with mean and standard deviation

Let be the average water consumed by a sample of n=100 males. Using the central limit theorem (since the sample size is greater than 30), we can say that has normal distribution with mean and standard deviation (or standard error of mean)

If you bring 210 L of water for 100 men, then we have on an average 2.1 L of water per person in the group.

the probability that you will run out is the probability that the average consumption of a sample of 100 is greater than 2.1L

Prepare the following sheet

Get this

ans:  the probability that you will run out is 0.1056