For this data set, find the mean, mode, median and inter-quartile range. 2, 5, 6, 4, 7, 4, 7, 2, 8, 9, 4, 11, 9, 9, 6 Q1
For this data set, find the sample variance and sample standard deviation. 89, 47, 164, 296, 30, 215, 138, 78, 48, 39 Q2
In a study on speed control, an experimenter records two variables speed (miles/hour) and braking distance (feet), to understand the distance required to completely stop a vehicle at various speeds. State the independent variable and the dependent variable. Q3
In a study on speed control, an experimenter records two variables speed (miles/hour) and braking distance (feet), to understand the distance required to completely stop a vehicle at various speeds. The experimenter obtains the regression line with equation y = 6.45x 151.9. What does 6.45 mean in this context? Q4
In a study on speed control, an experimenter records two variables speed (miles/hour) and braking distance (feet), to understand the distance required to completely stop a vehicle at various speeds. The experimenter obtains the r value of 0.966. Comment on the relationship of the two variables. Q5
In how many ways can the letters from the word PRACTICE be arranged? Q6
In how many ways can 2 letters from the word DESSERTS be chosen? Q7
In how many ways can 3 letters from the word DESSERTS be chosen? Q8
In how many ways can the letters from the word DESSERTS be arranged such that the letters S are together? Q9
In how many ways can the letters from the word DESSERTS be arranged such that the letters R and T are together? Q10
In how many ways can the letters from the word PRACTICE be arranged such that the letters C are separated? Q11
In how many ways can the letters from the word PRACTICE be arranged such that the vowels A, E, I are separated? Q12
A fair coin is tossed 4 times. Let X be the number of heads obtained. State the distribution of X and find the mean and variance of X. Q13
A fair coin is tossed 4 times. Let X be the number of heads obtained. Give 3 conditions for X to be modelled by a Binomial distribution. Q14
77% of workers in a company drive to work. Choose 8 workers at random. Find the probability that all of them drive to work. Q15
77% of workers in a company drive to work. Choose 8 workers at random. Find the probability that exactly 3 drive to work. Q16
77% of workers in a company drive to work. Choose 8 workers at random. Find the probability that more than one-half drive to work. Q17
The number of calls received per day at a crisis hotline centre is distributed as follows: x 30 31 32 33 34 P X = x 0.05 0.21 k 0.25 0.11 ( ) Find the values of k, mean of X and variance of X. Q18
A bag contains 4 red balls and 2 white balls. Three balls are drawn at random, one by one and without replacement. Draw a tree diagram to show the outcomes of the draws. Q19
A bag contains 4 red balls and 2 white balls. Three balls are drawn at random, one by one and without replacement. Use your tree diagram to find the probability of getting 2 red balls given that the second ball is red. Q20
1 2 3 Events A and B are such that P( A ) =, P( B A ) = and P( A' B' ) =. 4 5 10 Draw a Venn diagram showing all possible probability values, supported by working. Q21
The number of cars caught speeding per day, by a particular camera, has a Poisson distribution with mean 0.8. Find the probability that 2 cars will be caught by this camera on each of 4 randomly chosen consecutive days. Q22
The number of cars caught speeding per day, by a particular camera, has a Poisson distribution with mean 0.8. Find the probability that more than 2 cars will be caught by this camera on each of 4 randomly chosen successive days. Q23
The number of cars caught speeding per day, by a particular camera, has a Poisson distribution with mean 0.8. Find the probability that in a given 4-day period, exactly 3 cars will be caught by this camera. Q24
The number of cars caught speeding per day, by a particular camera, has a Poisson distribution with mean 0.8. Find the probability that in a given 4-day period, less than 3 cars will be caught by this camera. Q25
The number of cars caught speeding per day, by a particular camera, has a Poisson distribution with mean 0.8. Give 3 conditions for a Poisson model to be valid in this context. Q26
Use the standard normal table to find P( Z < 1.65). Q27
Use the standard normal table to find P( Z > 1.91). Q28
Use the standard normal table to find P( 0 Z 2.32) < <. Q29
Use the standard normal table to find m such that P( Z m) 0.5478 < =. Q30
Use the standard normal table to find m such that P( Z m) 0.8212 > =. Q31
Use the standard normal table to find m such that P( m Z ) < < 1.56 = 0.5199. Q32
In a normal distribution, find σ when µ = 105 and 5.48% of the area lies to the right of 110. Q33
The weight of a child in a particular nursery school is normally distributed with mean 13 kg and standard deviation 2 kg. A random sample of 20 children is taken. State the distribution of the mean weight of this sample. Q34
The weight of a child in a particular nursery school is normally distributed with mean 13 kg and standard deviation 2 kg. A random sample of 20 children is taken. Find the probability that the mean weight of this sample is between 12.5 kg and 14 kg. Q35
The 11 letters in the word MATHEMATICS are arranged randomly. Find the probability that a randomly picked arrangement has a vowel as the last letter. Q36
The waiting time to be seated for dinner at a popular restaurant is normally distributed with mean 23.5 minutes and standard deviation 3.6 minutes. Find the probability that a customer will have to wait for less than 18 minutes or more than 25 minutes. Q37
Events A and B are such that P( A ) = 0.7, P( B ) = 0.4 and P( A B) 0.82 Are A and B independent? Explain, with clear working steps. =. Q38
If X ~ (, ) B n p, state (a) the name of the probability model, (b) what n and p refer to, (c) E ( X ) and ( ) (e) P( X x) Var X in terms of n and p, = in terms of x, n and p, EGB207 Engineering Mathematics 2C (f) the distribution of X whose sample size is 49, in terms of n and p. Q39
If X ~ ( ) Po µ, state (a) the name of the probability model, (b) what µ refers to, (c) σ in terms of µ, (e) P( X x) = in terms of x and µ, EGB207 Engineering Mathematics 2C (f) the distribution of X whose sample size is 49, in terms of µ. Q40
A and B are two random events. Fill in the blanks for each. (a) P( A' ) = (b) P( A B) (c) P( B A ) = = (d) A, B mutually exclusive means that (e) A, B not independent means that Q41
A gardener measures the time taken, y minutes, for 60 grams of weed killer pellets to dissolve in 10 litres of water at different set temperatures, x C, where 16 x 56. Excel summary output shows the following data. Multiple R: 0.995406734 Intercept: 5.950909091 X Variable 1: 0.087272727 State the equation of the line of best fit, y = a + bx. Q42
A gardener measures the time taken, y minutes, for 60 grams of weed killer pellets to dissolve in 10 litres of water at different set temperatures, x C, where 16 x 56. Excel summary output shows the following data. Multiple R: 0.995406734 Intercept: 5.950909091 X Variable 1: 0.087272727 If the equation of the line of best fit is y = a + bx, interpret the meaning of b in this context. Q43
A gardener measures the time taken, y minutes, for 60 grams of weed killer pellets to dissolve in 10 litres of water at different set temperatures, x C, where 16 x 56. Excel summary output shows the following data. Multiple R: 0.995406734 Intercept: 5.950909091 X Variable 1: 0.087272727 Comment on the relationship between x and y. Q44
A gardener measures the time taken, y minutes, for 60 grams of weed killer pellets to dissolve in 10 litres of water at different set temperatures, x C, where 16 x 56. Excel summary output shows the following data. Multiple R: 0.995406734 Intercept: 5.950909091 X Variable 1: 0.087272727 Use the regression line to estimate the time taken to dissolve 60 grams of weed killer pellets in 10 litres of water at 75 C. Is the estimate reliable? Q45
A gardener measures the time taken, y minutes, for 60 grams of weed killer pellets to dissolve in 10 litres of water at different set temperatures, x C, where 16 x 56. Excel summary output shows the following data. Multiple R: 0.995406734 Intercept: 5.950909091 X Variable 1: 0.087272727 Use the regression line to estimate the time taken to dissolve 60 grams of weed killer pellets in 10 litres of water at 50 C. Is the estimate reliable? Q46
For this data set containing satisfaction scores on a scale of 1 to 10, explain which measure mean or median better represents it? 1, 3, 3, 3, 3, 5, 9, 10, 10 Q47
John bought tickets for Ed Sheeran s concert for himself, his wife, 2 male friends, and 3 female friends. In how many ways can they be seated in a row if there are 2 friends between John and his wife. Q48
Air bubbles occur in glass panels during its production. The number of air bubbles in a glass panel may be modelled as having a Poisson distribution with mean 1.3. Find the probability that, out of 12 randomly chosen glass panels, 3 of them contain at most 2 air bubbles. Q49
A drawer contains 8 brown socks and 4 blue socks. A sock is taken from the drawer at random, its colour is noted and it is then replaced. This procedure is performed twice more. If X is the random variable the number of brown socks taken, construct the probability distribution for X. Q50
A drawer contains 8 brown socks and 4 blue socks. A sock is taken from the drawer at random, its colour is noted and it is then replaced. This procedure is performed twice more. If X is the random variable the number of brown socks taken, calculate µ and σ. Q51
Is there a need to use Central Limit Theorem for each of these situations? Explain. Situation 1: The lengths of bolts produced by a machine have a mean of 3.03 cm and a standard deviation of 0.20 cm. A sample of 100 bolts is taken. Find the probability that the mean length of this sample is less than 3 cm. Situation 2: The lengths of bolts produced by a machine are normally distributed with mean 3.03 cm and standard deviation 0.20 cm. A sample of 5 bolts is taken. Find the probability that the mean length of this sample is less than 3 cm. Q52