PROBABILITY AND STATISTICS — Summer 2021

An MBA applies for a job in two firms Xand Y. The probability of his being selected in firm Xis 0.7 and being rejected in Yis 0.5. The probability of at least one of his applications being rejected is 0.6. What is the probability that he will selected in one the firms?

Astudy showed that 65%of managers had some business education and 50% had some engineering education. Furthermore 20% the managers had some business education but no engineering education. What is the probability that a manager had some business education, given that he has some engineering education?

Amanufacturing firm produces steel pipes in three plants with daily production volume of 500, 1000, 2000 units respectively. According to past experience it is know that the fractions of defective output produced the three plants are respectively 0.05, 0.08, and 0.10. If a pipe is selected from a day’s total production and found to be defective. What is the probability that it came from the first plant? Also find out from which plant the defective pipe comes.

The probability that an item produced by a machine will be defective is . If 12 such items are produced, find the probability that (i) Exactly10 one will be defective, (ii) at least two will be defective (iii) None of the item is defective.

Acar hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 𝜇 = 1.5. Calculate the proportion of days on which neither car is used and proportion of days on which some demand is refused. (e−1.5 = 0.2231)

The average daily sales of 500 branch offices was Rs. 150 thousand and the standard deviation Rs. 15 thousand. Assuming the distribution to be normal indicate how many branches have sales between

Rs. 120 thousand and Rs. 145 thousand

Rs. 140 thousand and Rs. 165 thousand. P(0<z<2)=0.4772, P(0<z<0.33)=0.1293, P(0<z<1)=0.2486

Accidents occur with a Poisson distribution at an average 2 per week. Then

Obtain the probability of more than 3 accidents during a week.

What is the probability that at least two weeks will elapse between accidents.

Afair die is thrown 300 times. Find the lower bound for the probability of getting 30 to 60 sixes.1

Find the quartile deviation and its coefficients. Also find inter quartile range and coefficient of variations. Marks < 35 35-37 38-40 41-43 > 43 Students 8 16 13 8

The following data relate to the profits of 1,000 companies: Profits Rs. 100- 120- 140- 160- 180- 200- 220- in 120 140 160 180 200 220 240 thousands No. of 17 53 199 194 327 208 companies Calculate the coefficient of skewness.

Following is the table showing number of visitors in 180 days to a zoo. Obtain average number of visitors per day. Marks 1-10 11-20 21-30 31-40 41-50 51-60 Students 22 28 35 45 30

Define moments about the assumed mean A. Obtain fist four moments about arbitrary origin from the following table, Scorers 50-60 60-70 70-80 80-90 90-100 Players 8 11 18 09

Find the mean, median and mode from the following table. class 50- 53- 56- 59- 62- 65- 68- 71- 74- frequency 3 8 14 30 36 28 16 10

Airscrew escape systems powered by a solid propellant. The burning rate of this propellant is an important product characteristics. Specifications require that the mean burning rate must be 50 centimeters per second and standard deviation of burning rate  centimeters per second. The experimenter choose 0.05 level of significance and selects random sample of n25and obtain a sample average of x51.3centimeters per second. What conclusions should be drawn? (z 1.96) 0.025

Psychological tests of intelligence and of engineering ability were applied to 10 students as per the following data. Find the coefficient of correlation. Intelligence 105 104 102 101 100 99 98 96 93 92 ration Engineering 101 103 100 98 95 96 104 92 97 94 ability

The following table gives the aptitude test scores and productivity indices of 10 workers selected at random Aptitude 60 62 65 70 72 48 53 73 65 82 scores Productivity 68 60 62 80 85 40 52 62 60 81 index Estimate (i) the productivity index of a worker whose test score is 0.92 (ii) the test score of a worker whose productivity index is 0.75.

You are working as a purchase manager for a company. The following information has been supplied to you by two manufactures of electric bulbs. Company A Company B Mean life in hours 1300 1248 Standard deviation 82 932 Sample size 100 100 Which brand of bulbs are you going to purchase if you desire to take a risk at 5%? ( Z = ±1.96) 0.05

An examination of eight applicants for a critical post was given by a firm. From the marks obtained by the applicants in the Accountancy and Statistics papers, compute rank coefficient correlations. Marks in 15 20 28 12 40 60 20 80 accountancy Marks in 40 30 50 30 20 10 30 60 statistics

500 units from a factory are inspected and 12 are found to be defective, 800 units from another factory are inspected and 12 are found to be defective. Can it be concluded at 5% level of significance that production at second factory is better that in first factory. ( Z = 0.05 ±1.96)

Two salesmen Aand Bare working in a certain district. From a sample survey conducted by the head office, the following results were obtained. Whether is there any significant difference in the average sales between two salesmen’s? A B Number of sales 20 18 Average sales in Rs. 170 205 Standard deviation in Rs. 20 25 The critical value of t at 5% level of significance and 36 degree of freedom is more than 36.

Asimply supported beam carries a concentrated load P(lb) at its mid- point. Corresponding to various values of Pthe maximum deflection y (in) is measured. The corresponding table is given below. Find the low of the y = a +bP. P 100 120 140 160 180 200 y 0.45 0.55 0.60 0.70 0.80 0.85

Arandom sample of size 15 from a bivariate normal population gave correlation coefficient r=0.5. Is this indicate the correlation in the population? Choose 0.05as level of significance,   t  2.160 2,13

By the method of least square fit a curve of the form y = axb to the following data. x 2 3 4 y 27.8 62.1 110 161