CHAPTER 1. Find the mean, median and mode for the number of returns prepared by each accountant.

Transcription

1 CHAPTER 1 TUTORIAL 1. Explain the term below : i. Statistics ii. Population iii. Sample 2. A questionnaire provides 58 Yes, 42 No and 20 no-opinion. i. In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers? ii. How many degrees would be in the section of the pie showing the No answers? iii. Construct pie chart. 3. Consider the following sample data: 4,14,6,9,21,3,7 and 10. What is the mode? 4. The accounting firm of Rowatti and Koppel specializes in income tax returns for selfemployed professionals, such as physicians, dentists, architects and lawyers. The firm employs 11 accountants who prepare the returns. For last year, the number of returns prepared by each accountant was : Find the mean, median and mode for the number of returns prepared by each accountant. 5. The Philadelphia office of Price Waterhouse Coopers LLP hired five accounting trainees this year. Their monthly starting salaries were $3536, $3173, $3448, $3121 and $3622. i. Compute the population mean. ii. Compute the population variance iii. Compute the population standard deviation. 6. The following table gives the frequency distribution of the number of hours spent per week playing video games by all 50 students of the eights grade at a school. Hours per Number of Students Week Find the mean, variance and standard deviation. Also, develop the histogram.

2 7. A company counted the number of all of their employees in each of the following age classes. According to the distribution, calculate mean, median, mode. Age Range Number of Employees The final results in business statistics of 40 students are recorded as below i. Present the data in frequency table. ii. Construct a histogram. iii. Calculate the mean, median, mode, variance and standard deviation.

3 9. The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows. Collision Payment ($) Probability a) Is this probability distribution valid? Explain. b) What is probability if collision payment is $5000? c) What is the probability that collision payment is make less than or equal to $5000? d) What is expected value or mean for collision payment? e) Compute the standard deviation of collision payment. 10. Let x be the number of cars that a randomly selected auto mechanic repairs on a given day. The following table lists the probability distribution of x. x P(x) a) Is this probability distribution?explain. b) What is the probability if the number of cars is 4? c) What is the probability if the number of cars is less than 5? d) What is the probability if the number of cars at most 3? e) What is the probability if the number of cars is at least 4 and less than 6?

4 f) Determine the cumulative discrete probability distributions. g) What is the expected value for the number of cars? h) Compute the variance and standard deviation of the number of cars? 11. Let X P (12). 0 Find using Poisson Table. a) PX ( 8) and PX ( 8) b) P(4 X 14) 12. On the average, 12 people per hour approach a decorating consultant questions in a fabric store. What is the probability that at least three people will approach the consultant with questions during 10-minute period? 13. Suppose that 0.03% of plastic containers manufactured by a certain process have small hotels that render them unfit for use. Let X represent the number of containers in a random sample of have this defect. Find a) PX ( 3) b) PX ( 2) c) P(1 X 4) d) E( x), Var( x ) 14. Determine the probability or area for the portions of the normal distribution described. a) P(0 Z 0.91) b) P( 1.01 Z 0) c) P( 1.2 Z 1.61) 15. Determine Z such that a) P( Z ) 0.35 Z b) P( Z ) 0.12 Z 16. The heights of boys at a particular age follow a normal distribution with mean 150.3cm and variance 25 cm. Find the probability that a boy picked at random from this age group has height a) Less than 153 cm b) More than 158 cm c) Between 150cm and 158 cm d) More than 10 cm difference from the mean height

5 17. 10% of the chocolate produced in a factory are mis-shapes. A random sample of 1000 chocolates taken. Find the probability that a) Less than 80 are mis-shapes b) Between 90 and 115 (inclusive) are mis-shapes c) 120 or more are mis-shapes 18. The number of calls per hour received by an office switchboard follows a Poisson distribution with parameter 30. Using the normal approximation to the Poisson distribution, find the probability that, in one hour a) There are more than 33 calls b) There are between 25 and 28 calls c) There are 34 calls 19. The amount of time required to change the oil and filter of any vehicles is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. a) What is the standard error of the sample mean to be? b) What is the probability of the sample mean between 45 and 52 minutes? c) What is the probability of the sample mean between 39 and 48 minutes? d) Find two values between the middle 95% of all sample means. 20. A random sample size 35 is drawn from a normal distribution with mean 30 and variance 25. What is the probability that a) The sample mean is at least 28? b) The sample mean is at most 32? c) The sample mean is between 29 and 32? 21. A certain type of thread with mean tensile strength of 78.3kg and standard deviation of 5.6kg is manufactured by machine A. Machine B produces a certain type of thread with mean tensile strength of 77kg and standard deviation of 4kg. A sample size of 40 thread are taken from machine A and machine B. What is the probability that a) The difference between mean tensile strength produced by machine A and machine B is smaller than 2kg?

6 b) The mean tensile strength produced by machine A is bigger than the mean tensile strength produced by machine B. 22. According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. a) What is the average of all the sample proportions of customers who will make a purchase after visiting the web site? b) What is the standard deviation of all the sample proportions of customers who will make a of purchase after visiting the web site? c) What is the probability that the proportion will have between 20% and 30% of customers who will make a purchase after visiting the web site?