Question 874801: The average monthly sales of 5000 firms are normally distributed with mean Rs. 36,000 and standard deviation Rs.10,000. Find
The number of firms with sales of over Rs.40,000
The percentage of firms with sales between Rs.38,500 and Rs. 41,000
The number of firms with sales between Rs. 30,000 and Rs 40,000.
Trading volume on the New York Stock Exchange has been growing in recent years. For the first two weeks of January 2008, the average daily volume was 646 million shares. The probability distribution of daily volume is approximately normal with a standard deviation of about 100 million shares.
What is the probability trading volume will be less than 400 million shares?
What percentage of the time does the trading volume exceed 800 million shares?
If the exchange wants to issue press release on the top 5% of trading days .what volume will trigger a release?
General hospital’s patient accounts division has compiled data on the age of account receivables. The data collected indicate that the age of the accounts flows a normal distribution with mean μ = 28 days and σ = 8 days.
What portion of accounts are between 20 and 40 days old?
The hospital administrator is interested in sending reminder letters to the oldest 15% of accounts. How many days old should an account be before a reminder letter is sent?
The hospital administrator wants to give a discount to those accounts that pay their balance by 21 st day. What percentage of the accounts will receive the discount?
The mean breaking strength of the cables supplied by a manufacturer is 1800 with a standard deviation 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In this claim a sample of 50 cables is tested . It is found that the mean breaking strength is 1850. Can we support the claim at 1 % level of significance?
An auto company decided to introduce a new six cylinder car whose mean petrol consumption is claimed to be lower than that of the existing auto engine. It was found that the mean petrol consumption for the 50 cars was 14 kms per litre with a standard deviation of 3.5 km per litre. Test for the company, whether the claim the new car petrol consumption is 13.4 km per litre on the average is acceptable.
In a certain factory there are two independent processes manufacturing the same item. The average weight in a sample of 250 items produced from one process is found to be 120 gms with a standard deviation of 12 gm. While the corresponding figure in a sample of 400 items from the other process are 124 gms and 14 gm. Is this difference between the mean weights significant at 1 % level.
In a survey of buying habits, 400 women shoppers are chosen at random in super market A located in a certain section of the city. Their average weekly food expenditure is Rs. 2500 with a S.D. of Rs. 400. For 400 women shoppers chosen at random in super market B in another section of the city , the average weekly food expenditure is Rs. 2200 with a S.D. of Rs 550.Test at 1 % level of significance whether the average weekly food expenditure of the population of shoppers are equal?
A random sample of 10 boys had the following I.Q’s: 70,120,110,101,88,83,83,95,98107,100.Do these data support the assumption of a population mean I.Q. of 100?Find a reasonable range in which most of the mean IQ values of samples of 10 boys lie.
A company is interested in knowing if there is a significant difference in the average salary received by managers in two divisions. Accordingly samples of 12 managers in the first division and 10 managers in the second division are selected at random,. Based upon experience managers’ salaries are known to be approximately normally distributed, and standard deviations are about the same.
` First division Second division
Sample size 12 10
Average monthly salary
of Managers(Rs.) 1050 980
Standard deviation of salaries(Rs) 68 74
A manufacturer claimed that at least 95 % of the equipments which he supplied to a factory conformed to specifications. An examination of a sample of 200 pieces of equipment revealed that 18 were faulty. Test his claim at a significant level of 0.01
A coin is tossed 100 times under identical conditions independently yielding 30 heads and 70 tails. Test at 1 % level of significance whether or not the coin is unbiased . State clearly the null hypothesis and the alternative hypothesis.
A company selects 8 salesmen at random and their sales figures (in thousand Rs.) for the previous month are recorded. They then undergo a course devised by a business consultant and their sales figures for the following month are compared as shown in the table. Has the training course caused an improvement in the salesmen’s ability? Use 5% level.
Previous month: 75 90 94 85 100 90 69 70
Following month: 77 98 93 92 105 88 73 76
Eight workers were given training programme with a view to shorten their assembly time for a certain mechanism. The results of the time and motion studies before and after the training programme are given below.
Worker : 1 2 3 4 5 6 7 8
First study : 15 18 20 17 16 14 21 19
(in mnts):
Second study: 14 16 21 10 15 18 19 16
(in mnts)
On this bases of this data can it be concluded that the training programme has shortened the average assembly time.
The following table gives the number of good and bad parts produced by each of three shifts in a factory.
Shift Good Bad Total
Day 900 130 1030
Evening 700 170 370
Night 400 200 600
Total 2000 500 2500
Is there any association between the shift and the equality of parts
produced?
Use Chi-square test to test if the two attributes in the following contingency table are independent.
Training
Performance Intensive Average Nominal
Above average 100 150 40
Average 100 100 100
Poor 50 80 150
The following data relate to the sales in a time of trade depression a certain article in great demand. Do the data suggest that the sales are significantly affected by depression?
District where
sales are Not hit by Hit by
Depression Depression
Satisfactory 140 60
Not satisfactory 60 40
A sample of 300 students of under graduate and 300 students of post graduate classes of a university were asked to give their opinion towards granting of autonomous status to its constituent colleges. 190 of the under graduate and 210 of the post graduate students favored the autonomous status.
Present the above facts in the form of a frequency table and test at 5 % level of significance that the opinions of the under graduate and the post graduate students on the autonomous status of colleges are independent.
In a class , there were 80 students . Among them, 18 students passed in preparatory examination. Whereas, in the final(Board) examination, 63 students passed. However, among those who passed the preparatory examination, only 16studentrs passed in the final examination,. Test at 1% level of significance whether passing in the preparatory examination and passing in the final examination are independent.
The following table gives the number of car accidents that occurred during the various days of the week. Find whether the accidents are uniformly distributed over the week.
Day: Sun Mon Tue Wed Thu Fri Sat
No. of accidents: 14 16 08 12 11 09 14
The following figures show the distribution of digits in numbers chosen at random from a telephone directory.
Digit : 0 1 2 3 4 5 6 7 8 9
Frequency: 1026 1107 997 966 1075 933 1107 972 964 853
The following data show the experience of machine operators and their performance ratings as given by the number of good parts turned out per 100 pieces.
Operator : 1 2 3 4 5 6 7 8
experience(X) : 16 12 18 4 3 10 5 12
performance : 87 88 89 68 78 80 75 83
rating(y)
Calculate the regression line of performance ratings on experience and estimate the probable performance if an operator has 10 years’ experience.
The following table gives the aptitude test scores and the productivity indices of 6 workers selected at random.
Aptitude Index(X) : 60 62 65 70 72 48
Productivity Index(Y): 68 60 62 80 85 40
a)What are dependent and independent variables?
b)Fit regression of Y on X
c)estimate the average productivity of a worker whose test score is 82.
d)Calculate the coefficient of determination and interpret
e)conduct a test to determine whether relation between X and Y is significant.
Calculate the coefficient of correlation from the following data and interpret the value
Advertising expenditure: 10 12 13 23 27 30
(Rs. In lakhs)
Sales turnover : 40 42 40 45 48 50
(Rs. In crores)
The following data show the experience of machine operators and their performance ratings as given by the number of good parts turned out per 100 pieces.
Operator : 1 2 3 4 5 6 7 8
experience(X) : 16 12 18 4 3 10 5 12
performance : 87 83 88 89 68 78 80 75
rating(y)
Calculate the regression line of performance ratings on experience and estimate the probable performance if an operator has 10 years’ experience.
The following table gives the aptitude test scores and the productivity indices of 6 workers selected at random.
Aptitude Index(X) : 60 62 65 70 72 48
Productivity Index(Y) : 68 60 62 80 85 40
a)What are dependent and independent variables?
b)Fit regression of Y on X
c)estimate the average productivity of a worker whose test score is 82.
d)Calculate the coefficient of determination and interpret
e)conduct a test to determine whether relation between X and Y is significant.
The following is an estimated supply regression for sugar
Y = 0.025 + 1.25 X
Where Y is supply in kilos and X is price(Rs.) per kilo.
a)Interpret the coefficient of variable X
b)Predict the supply when price is Rs 20 per kilo
Calculate the Rank correlation coefficient between advertisement cost and sales as per the data given below.
Advertisement cost in ‘000 Rs. 39 65 62 90 82 75 35 98
Sales in Rs. Lakhs 47 53 58 86 62 68 60 91
Ten competitors in a beauty contest are ranked by three judges in the following order
1st Judge: 1 6 5 10 3 2 4 9 7 8
2nd Judge: 3 5 8 4 7 10 2 1 6 9
3rd Judge: 6 4 9 8 1 2 3 10 5 7
Use the rank correlation coefficient to determine which pair of judges has the nearest approach to common tastes in beauty.
An examination of eight applicants for a clerical post was taken by a firm .from the marks obtained by the applicants in the Accountancy and Statistics papers, compute rank coefficient of correlation.
Applicant: A B C D E F G H
Marks in
Accountancy: 15 20 28 12 40 60 20 28
Marks in
Statistics : 40 30 50 30 30 40 35 48
Fit a Linear trend by the method of least squares to the data given below and project the probable sales for the next two years.
Year 2001 2002 2003 2004 2005
Sales(in ’000 Rs.) 164 180 186 190 185
Find 3 yearly and 4 yearly moving averages for the following data
Year 1998 1999 2000 2001 2002 2003 2004 2005
Sales 54 40 47 48 42 42 36 42
Answer by Fombitz(32388)   (Show Source):
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