Practice Test


1) The distribution of total probability over different mass points or class intervals is called -


2) Probability distribution is defined only for -


3) Theoretical distribution possess all the characteristics of an


4) __________ is a Discrete Probability Distribution


5) ___________is a Continuous Probability Distribution


6) Theoretical distributions are used to make future projections.


7) Trial is an attempt to produce particular outcome which is


8) Binomial distribution is a ______________ distribution.


9) Binomial distribution is


10) Characteristics of Bernoulli trial are


11) Mean = Variance this is true for


12) In case of Bernoulli trial the outcomes of the trials are


13) When p=0.5 the maximum value of variance is


14) In B(n,p) variance will always be ____________ mean.


15) If for a Binomial distribution (n+1)p is a non - integer then mode of that distribution is


16) Binomial distribution is applicable only when


17) Poisson distribution was introduced by


18) Poisson distribution is known as _____________ distribution.


19) Poisson distribution is


20) In Poisson distribution if "m" is non - integer then mode =


21) In poisson distribution the number of trials tends to infinity.


22) In Binomial and Poisson Distribution, mean = np


23) The condition not satisfied by a random experiment of poisson distribution are


24) In the x ~ P(m) the value probability of success (p) is very


25) In Poisson distribution if m is an integer mode is


26) For finding distribution of the number of spade cards when a card is drawn from a pace of 52 cards for 5 times the method is


27) The following are continuous probability distributions : Normal, Chi-square, t-distribution and F-distribution


28) Normal distribution was mainly derived by


29) Normal distribution is


30) Binomial distribution is symmetrical when


31) Normal curve is a symmetrical curve


32) Normal curve is bell shaped and has multi peaks


33) Total area of the normal curve is taken as


34) Total area of any probability curve is taken as


35) Normal distribution is


36) For an asymmetrical distribution


37) For an symmetrical distribution


38) If the distribution is asymmetrical then the skewness is zero


39) If the distribution is symmetrical then the skewness is zero


40) Number of points of inflexion a normal curve has _________


41) For Normal distribution P(0 < z < 1) is


42) For Normal distribution P(-3 < z < 3) is


43) The point at which normal curve changes its curvature from convex to concave is called


44) For a standard normal distribution the points of inflexion are at


45) When p=0.8 the Binomial distribution is


46) When p=0.25 the Binomial distribution is Skewed towards


47) The number of observations that can be chosen without any restriction is called


48) Chi - square distribution is used for


49) Chi - square distribution is always


50) Mean of t-distribution is


51) t-distribution is ____________ about t=0


52) If the probability that any person 40 years old will be dead within a year is p=0.01. Find the probability that out of a group of 7 such persons, none will die within one year.


53) If the probability that any person 40 years old will be dead within a year is p=0.01. Find the probability that out of a group of 7 persons; exactly one will die within one year.


54) If the probability that any person 40 years old will be dead within a year is p=0.01. Find the probability that out of a group of 7 persons; not more than one will die within one year.


55) If the probability that any person 40 years old will be dead within a year is p=0.01. Find the probability that out of a group of 7 persons; more than one will die within one year.


56) If the probability that any person 40 years old will be dead within a year is p=0.01. Find the probability that out of a group of 7 persons; at least one will die within one year.


57) Out of 1000 families of 3 childern each, how many families would you expect to have 2 boys and girl are equally likely?


58) If hens of a certain breed lay eggs on 5 days a week on an average, find how many days during a season of 100 days, a poultry keeper with 5 hens of hens of their breed will expect to receive at least 4 eggs?


59) It is observed that 4 % of the students of a certain class wear glasses. If 5 students of this class are selected at random, what is the chance that among them, at least one wear glasses?


60) The incidence of occupational disease in an industry is such that the workers have a 20 % chance of suffering from it. What is the probability that out of six workers 4 or more will catch the disease?


61) It is observed that one out of four persons requires on an average medical help. Find the probability that at least one person out of three requires medical help.


62) It is observed that one out of four persons requires on an average medical help. Find the probability that only one person out of three requires medical help.


63) In a large consignment of bolts, 10 % are defective. In a sample of 4 bolts drawn at random from the consignment, find the probability that the sample contains no defective bolts.


64) In a large consignment of bolts, 10 % are defective. In a sample of 4 bolts drawn at random from the consignment, find the probability that the sample contains at least one defective bolt.


65) If the probability of a defective bolt is 1/10. find the following for the Binomial distribution of defective bolts in a total of 400 : (i) mean, (ii) S.D


66) In a Binomial distribution with 6 independent trails, the probability of 3 and 4 successes are found to be 0.2457 and 0.0819 respectively. Find the parameter p of the Binomial


67) If we take 1280 sets each of 10 tosses of a coin, in how many sets, should we expect to get 7 heads and 3 tails?


68) The probability that a student is not a swimmer is 20 %. Out of 5 students selected. Find the probability that (a) 4 are swimmers.


69) The probability that a student is not a swimmer is 20 %. Out of 5 students selected. Find the probability that at least 4 are swimmers.


70) Take 100 sets of 10 tosses of an unbiased coin. In how many tosses do you expect to get 8 or more heads?


71) Three fair coins are tossed 3000 times. Find the frequencies of the distribution of heads and tails and tabulate the result.


72) Three fair coins are tossed 3000 times. Find mean and S.D. of the distribution.


73) A box contains 100 bolts of which 10 are defective. Find the probability that a bolit chosen at random is not defective.


74) Examine the validity of the following statement: mean of a binomial distribution is 10 and standard deviation is 4.


75) Suppose that sizes of hats are approximately normally distribution with mean of 18.5 cm and a s.d. of 2.5 cm. how many hats in the total of 2000 will have sizes between 18 cms and 20 cms? (Area between z=0 and z=0.6 is 0.2257 and the area between z=0 and z=0.2 is 0.793 where z is the standard normal variate


76) Suppose that sizes of hats are approximately normally distribution with mean of 18.5 cm and a s.d. of 2.5 cm. how many hats in the total of 2000 will have sizes more than 20 cms? (Area between z=0 and z=0.6 is 0.2257 and the area between z=0 and z=0.2 is 0.0793 where is the standard normal variate)


77) Earnings of 10000 persons conform to the normal curve with mean of Rs.750 p.m. and s.d. of Rs.50. finds the number of persons with income exceeding Rs. 670? (Given that area between z= 0 and z=1.6 is 0.4452; area between z= 0 and z=0.6 is 0.2257; area between z=0 and z=2.33 is 0.49)


78) Earnings of 10000 persons conform to the normal curve with mean of Rs.750 p.m. and s.d. of Rs.50. finds the number of persons with income not less than Rs.720. (Given that area between z= 0 and z=1.6 is 0.4452; area between z= 0 and z=0.6 is 0.2257; area between z= 0 and z=2.33 is 0.49)


79) Earnings of 10000 persons conform to the normal curve with mean of Rs.750 p.m. and s.d. of Rs.50. finds the number of persons with income what is the highest income of the poorest 100 persons. (Given that area between - z=0 and z=1.6 is 0.4452; area between z=0 and z=0.6 is 0.2257; area between z=0 and z=2.33 is 0.49)


80) The weights of 4000 students are found to be normally distributed with mean 50 kgs. And S.D. 5 kgs. Find the number of students with weights less than 45 kgs. (You are given the area under z=0 to z=1 is 0.3413 and z=0 and z=2 is 0.4772)


81) The weights of 4000 students are found to be normally distributed with mean 50 kgs. And S.D. 5 kgs. Find the number of students with weights between 45 and 60 kg. (You are given the area under z= 0 to z= 1 is 0.3413 and z=0 and z=2 is 0.4772)


82) A census of rentals for apartments in a city follows a normal distribution with mean Rs.800 and s.d. Rs.100. what is the probability that an apartment selected at random will have its rent between Rs.800 and Rs.1000? (Area between t=0 and t=2 is 0.4772; t=0 and t=1 is 0.3413; t=0 and t=1.5 is 0.4332)


83) A census of rentals for apartments in a city follows a normal distribution with mean Rs.800 and s.d. Rs.100. what percentage of apartment will have their rent between Rs.600 and Rs.900? (Area between t=0 and t=2 is 0.4772; t=0 and t=1 is 0.3413; t=0 and t=1.5 is 0.4332)


84) A census of rentals for apartments in a city follows a normal distribution with mean Rs.800 and s.d. Rs.100. what percentage of apartment will have their rent below Rs.650? (Area between t=0 and t=2 is 0.4772; t=0 and t=1 is 0.3413; t=0 and t=1.5 is 0.4332)


85) The I.Q. scores of 1500 applicants for admission to a tuition-free graduate school are normally distributed with a mean of 125 and a standard deviation of 10. What percentage of applicants will have their I.Q. between 125 and 135?


86) The I.Q. scores of 1500 applicants for admission to a tuition-free graduate school are normally distributed with a mean of 125 and a standard deviation of 10. What are the limits of I.Q. for the middle 50 per cent applicants?


87) Average daily sales for a shop follow a normal distribution. It is given that the probability that the average daliy sale is less than Rs.124 is 0.0228 and the probability that it exceeds 331 is 0.1587. find the mean and the standard deviation of the distribution. (Area between t= 0 and t=1 is 0.3413. Area between t=0 and t=2 is 0.4772)


88) The heights of 1000 cakes baked with a certain mix have a normal distribution with mean of 5.75 cms. And a student's deviations of 0.75 cm. Find the maximum heights of the flattest 200 cakes. (For a standard normal variate t, the area between t=-1 and t=1 is 0.6826; the area between t=0 and t=0.67 is 0.2486 and the area between t=0 and t=0.84 is 0.3000)


89) The heights of 1000 cakes baked with a certain mix have a normal distribution with mean of 5.75 cms. And a student's deviations of 0.75 cm. Find the number of cakes having heights between 5 cms and 6.25 cms. (For a standard normal variate t, the area between t=-1 and t=1 is 0.6826; the area between t=0 and t=0.67 is 0.2486 and the area between t=0 and t=0.84 is 0.3000)


90) The income of a group of 10000 persons were found to be normally distribution with mean Rs.500.00 and standard deviation Rs.60. Find the number of persons having incomes between Rs.400 and Rs.500. (For a standard normal variate t , the area under the curve between t=0 and t=0.5 is 0.19146, the area between t=0 and t=1.645 is 0.45000 and the area between t=0 and t=2 is 0.47725, Area between t=0 and t=1.67 is 0.4525.)


91) The incomes of a group of 10000 persons were found to be normally distribution with mean Rs.500.00 and standard deviation Rs.60. Find the lowest income of the richest 500. (For a standard normal variate , the area under the curve between t=0 and t=0.5 is 0.19146, the area between t=0 and t=1.645 is 0.45000 and the area between t=0 and t=2 is 0.47725, Area between t=0 and t=1.67 is 0.4525.)


92) What are the characteristics of a normal curve? If the heights of 1000 soldiers in a regiment are distributed normally with a mean of 172 cms and a standard deviation 5 cms how many soldiers have heights greater than 180 cms? (The area of a standard normal variate t between t=-1.6 and t=1.6 is 0.8904)


93) The heights of 1000 soldiers in a regiment are distributed normally with a mean of 175 cms and s.d. 5 cms. How many soldiers are expected to have a height of 180 cms or more?


94) The heights of 1000 soldiers in a regiment are distributed normally with a mean of 175 cms and s.d. 5 cms. How many would be expected to be shorter than 170 cms?


95) The heights of 1000 soldiers in a regiment are distributed normally with a mean of 175 cms and s.d. 5 cms. How many will have their height between 165 cms and 185 cms?


96) Assume the mean height of soldiers to be 68.22 inches with a variance of 10.8 inches. How many soldiers in a regiment of 1000 would you expect to be over six feet tall? (Area under normal curve between t=0 and t=1.15 is 0.3749).


97) A hundred squash balls are tested by dropping from a height of 100 inches and measuring the height of bounce. A ball is "fast" if it rises above 32 inches. The average height of bounce was 30 inches and the standard deviation was 3/4 inches. What is the chance of getting a "fast" standard ball? (Area under normal curve between z= 0 and z=2.67 is 0.4962)


98) Suppose that X is a continuous variable with a normal distribution and has a mean of 10 and standard deviation equal to 2. What is the probability that the value of X selected at random lies between 9 and 12? (Area under normal curve between z=0 and z=1 is 0.3413 and z=0 and z=0.5 is 0.1915)


99) In a sample of 1000 items, the mean weight and standard deviation are 50 and 10 kgs respectively. Assuming the distribution the distribution to be normal, find the number of items weighing between 40 and 70 kgs.


100) For a normal distribution with mean 120 and S.D. 40, what is the probability of P(x<=(150/x)>120)? (Area under normal curve between z=0 and z=0.75 is 0.3734)


101) For finding distribution of the number of radio-active elements per minute in a fusion process the method used is


102) Binomial can be approximated by poisson distribution than


103) For a normal distribution the p.d.f is defined as


104) For a normal distribution the following is incorrect:


105) For Poisson distribution S.D is ___________


106) Mean of a chi-square distribution is


107) S.D. of a chi - square distribution is


108) S.D. of t-distribution is ______________, when n >2.


109) Mean of F-distribution is


110) If the probability that any person 40 years old will be dead within a year is p = 0.01. Find the probability that out of a group of 7 persons; all of them will be dead within year.