Product moment coefficient Level 0.05 0.025 0.01 0.005 0.9000 0.9500 0.9800 0.9900 0.8054 0.8783 0.9343 0.9587 0.7293 0.8114 0.8822 0.9172 0.6694 0.7545 0.8329 0.8745 0.6215 0.7967 0.7887 0.8343 0.5822 0.6664 0.7498 0.7977 Initially there are 10 beads in the bag and 6 are 6 green. P(G1) = __ ​​ 10 ​​ . Since a green bead is removed and not replaced, the total number of beads is reduced to 9 and there are just 5 green beads remaining. The probability that B occurs given that A has already occurred is written as P(B|A). For independent events, P(A|B) = P(A|B9) = P(A), and P(B|A) = P(B|A9) = P(B). 3 P(A ∪ B) = P(A) + P(B) − P(A ∩ B) Accessing a CGP Online Edition by using a code from a printed CGP book grants you access to the title for three years from the date of activation of the code.

These histograms show the distribution of heights of adult males in a particular city. As the class width reduces, the distribution gets smoother. A computer-controlled milling machine is calibrated between 1 and 7 times a week. A supervisor recorded the number of weekly calibrations, x, and the number of manufacturing errors, y, in each of 7 weeks. x c Tom says that the median is equal to the mean. State, with a reason, whether Tom is correct. E/P It is believed that there is a relationship between the age and maintenance cost of these machines. b Using a 5% level of significance and quoting from the table of critical values, interpret your correlation coefficient. Use a two-tailed test and state clearly your null and alternative hypotheses.  (3 marks) Ea P(C ∩ D) =  P(C|D) × P(D) = 0.3 × 0.6 = 0.18 P(D ∩ C) b P(D|C) = ​​ _________ ​​ P(C) 0.18 = _____ ​ ​ ​​ = 0.9 0.2 c P(C ∪ D) =  P(C) + P(D) − P(C ∩ D) = 0.2 + 0.6 − 0.18 = 0.62

d Determine whether the events J and K are statistically independent. You must show all your working. The data are coded using the changes of variable x = t and y = log g. The regression line of y on x is found to be y = −0.2215 + 0.0792x. a Mika says that the constant −0.2215 in the regression line means that the colony is shrinking when the temperature is 0 °C. Explain why Mika is wrong. b Given that the data can be modelled by an equation of the form g = kbt where k and b are constants, find the values of k and b. 2 M01_EDSM2_SB_AL_83282_U01_001-015.indd 2 If X = x then the corresponding value of Z will be x − μ µ−µ z = _____ ​​ σ .​​ The mean of the coded data will be ​​ _____ ​​ = 0 and σ σ ​​ σ ​​ = 1.  ← Year 1, Section 2.5 the standard deviation will be __ Finding probabilities for normal distributions You can find probabilities for a normal distribution using the normal cumulative distribution function on your calculator. Of 60 students in a high-school sixth form, 35 study French and 45 study Spanish. If 27 students study both, find the probability that a student chosen at random: a studies only one subject  Subtract this probability from a and b and write the probabilities on the Venn diagram as shown. The probability of A ∪ B is

Use the fact that the total probability is equal to 1. Sketch the two ‘tails’ of the required area. 27 30 32 a State the meaning of n/a in the table above. b Calculate the product moment correlation coefficient for the remaining 8 days. c With reference to your answer to part b, comment on the suitability of a linear regression model for these data. a Data on daily maximum gust is not available for these days.Two coins are flipped and the results are recorded. Given that one coin lands on a head, find the probability of: a two heads