Q1 Own your learning with flash cards.

Size: px

Start display at page:

Download "Q1 Own your learning with flash cards."

Maximilian Barton
6 years ago
Views:

1 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

2 For this data set, find the sample variance and sample standard deviation. 89, 47, 164, 296, 30, 215, 138, 78, 48, 39 Q2

3 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

4 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 What does 6.45 mean in this context? Q4

5 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 Comment on the relationship of the two variables. Q5

6 In how many ways can the letters from the word PRACTICE be arranged? Q6

7 In how many ways can 2 letters from the word DESSERTS be chosen? Q7

8 In how many ways can 3 letters from the word DESSERTS be chosen? Q8

9 In how many ways can the letters from the word DESSERTS be arranged such that the letters S are together? Q9

10 In how many ways can the letters from the word DESSERTS be arranged such that the letters R and T are together? Q10

11 In how many ways can the letters from the word PRACTICE be arranged such that the letters C are separated? Q11

12 In how many ways can the letters from the word PRACTICE be arranged such that the vowels A, E, I are separated? Q12

13 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

14 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

15 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

16 77% of workers in a company drive to work. Choose 8 workers at random. Find the probability that exactly 3 drive to work. Q16

17 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

18 The number of calls received per day at a crisis hotline centre is distributed as follows: x P X = x k ( ) Find the values of k, mean of X and variance of X. Q18

19 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

20 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

21 1 2 3 Events A and B are such that P( A ) =, P( B A ) = and P( A' B' ) = Draw a Venn diagram showing all possible probability values, supported by working. Q21

22 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

23 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

24 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

25 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

26 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

27 Use the standard normal table to find P( Z < 1.65). Q27

28 Use the standard normal table to find P( Z > 1.91). Q28

29 Use the standard normal table to find P( 0 Z 2.32) < <. Q29

30 Use the standard normal table to find m such that P( Z m) < =. Q30

31 Use the standard normal table to find m such that P( Z m) > =. Q31

32 Use the standard normal table to find m such that P( m Z ) < < 1.56 = Q32

33 In a normal distribution, find σ when µ = 105 and 5.48% of the area lies to the right of 110. Q33

34 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

35 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

36 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

37 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

38 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

39 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

40 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

41 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

42 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: Intercept: X Variable 1: State the equation of the line of best fit, y = a + bx. Q42

43 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: Intercept: X Variable 1: If the equation of the line of best fit is y = a + bx, interpret the meaning of b in this context. Q43

44 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: Intercept: X Variable 1: Comment on the relationship between x and y. Q44

45 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: Intercept: X Variable 1: 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

46 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: Intercept: X Variable 1: 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

47 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

48 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

49 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

50 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

51 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

52 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

Example. If 4 tickets are drawn with replacement from ,

Example. If 4 tickets are drawn with replacement from 1 2 2 4 6, what are the chances that we observe exactly two 2 s? Exactly two 2 s in a sequence of four draws can occur in many ways. For example, (