Relation between standard deviation of the sample and standard deviation of the population

    Example 1 • Consider the relation between standard deviation of the sample and standard deviation of the population • Be sure you understand the meaning of each variable. • Identify the given variables: mean standard deviation of the population size of the sample • With the given values you can compute the standard deviation of the mean. Example 2 • Consider the definition of z Z = • Consider the relation between standard deviation of the sample and standard deviation of the population • Identify the given variables • need to convert from the population standard deviation to standard deviation of the mean. Note: We consider the mean sample to be equal to the mean of the origin population. • Find Z (for the given X) • Find area under the curve • Compute the final answer. Keep in mind that you need the likelihood for or more than “ X” hours. Keep in mind that not all problems or sub-problems use a sample. Show all manual calculations and provide commentary to your answers. Don’t just give the final answer. Don’t use a specific software. Use the z-tables (non-cumulative or cumulative) and your knowledge on the subject PROBLEM 1 (10 points): The average time it takes a student to read the rules for entering the college is 15 minutes with a standard deviation 4 minutes. Suppose you take a random sample of 64 students. The standard deviation of the sample mean is: Standard Deviation PROBLEM 2 (15 points): A company that manufactures bookcases finds that the average time it takes an employee to build a bookcase is 4 hours with a standard deviation of 30 minutes. A random sample of 81 employees is taken. What is the likelihood that the sample mean will be less than 4 hours and 15 minutes? Probabilistic Likelihood PROBLEM 3 (15 points each sub-point): The average grade (GPA) of undergraduate students in New York is normally distributed with a population mean of 2.5 and a population standard deviation of 0.5. Compute the following, showing all work: (I) The percentage of students with GPA's above 2.0 is Choice (II) The percentage of students with GPA's below 2.7 is: Percentage (III) Above what GPA will the top 10% of the students be: GPA (IV) If a sample of 36 students is taken, what is the probability that the sample mean GPA will be between 2.25 and 2.75? Choice   PROBLEM 4 (15 points): At the end of the Spring Festival the organizers estimated that a family of participants spent in average $45.00 with a standard deviation of $8.00. If 49 participants (49 = size of the sample) are selected randomly, what’s the likelihood that their mean spent amount will be within $3 of the population mean? (mean +/- 3; between $42 and $48) Likelihood (probability)