1. If the average price of a new one family home is 246,300 with a standard eviation of $15,000 find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 62% of the market. Assume that the variable is normally distributed. Round value calculations to 2 decimal places for final answers to the nearest dollar.
2. To help students improve their reading a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district based on the scores on a reading achievement exam. If the average score for the students in the district is 121.9 find the cutoff score that will make a student eligible for the program. The standard deviation is 16. Assume the variable is normally distributed.
3. A mandatory competency test for high school sophmores has a normal distribution with a mean of 420 and a standard deviation of 120. Round the final answers to the nerest whole number and intermediate value
a. The top 7% of students receive $500. What is the minimum Score you would need to receive this award?
b. The bottom 3.5% of the students must go to summer school. What is the minimum score you would need to stay out of this group?
4. In order to qualify for a police academy, applicants are given a test of physical fitness. The scores are normally distributed with a mean of 68 and a standard deviation of 6. If only the top 25% of the applicants are selected find the cutoff score.
5. A survey found that the American family generate an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probablilty that the mean of a sample of 31 families will be between 17.2 and 18.2 pounds. Assume that the sample is taken from a lagre population and the correction factor can be ignored. Round your final answer to four decimal places and intermediate.
6. The average teacher's salary in Connecticut is 57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500. Round intermediate value calculations to two decimal places and the final answer to four decimal places.
7. A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its 36 employees with a cell phone, find the probablility that the mean lifetime of these phones will be less than 23.6 months. Assume cell phone life is a normally distributed variable, the sample is taken form a large poulation and the correction factor can be ignored. Round final answer to four decimal places and the intermediate z value calculations to two decimal places.
8. The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. Suppose the benefits are normally distributed with a standard deviation of $460. Round final answer to four decimal places and intermediate value calculation to two decimal places find the probability that the mean benefit for a random sample of 23 patients is less than 2820.
Find the probability that the mean benefit for a random sample of 21 patients is more than $3920
Find the probability that the mean benefit for a random 21 patients is more than 4250
9. At a large publishing company the mean age of proofreaders is 36.2 years and the standard deviation is 3.7 years. Assume the variable is normal distributed. Round intermediate value calculations to two decimal places and the final answers to four.
If the proofreaders form a company is randomly selected find the probability that his or her age will be between 34.5 and 36 years.
If a random sample of 18 proofreaders is selected, find the probability that the mean age of the proofreaders in the sample will be between 34.5 and 36 years. Assume that the sample is taken from a large population and correction factor can be ignored.