'1 statistics 2017 mid testpdf 7 Adobe Acrobat Reader DC — x

File Edit View Window Help Home Tools statistic52017 mid... >< C?) 73113 ' [EDGJBEIQ ©© 5 I6 9.? tiny that he works productively for more than 015 hours, he gets 5 points. Find A

Solution: the expected value of the number- of points Dirks gets each day.

0.8304

Solution:

(c) 3 marks] If W denotes the number of hours Dirk works productively today and 40051 5 denotes the number of hours Dirk sleeps today, ﬁnd the varianee of SW + 23. Solution: END OF EXAMINATION 12.16 Question 5 [13 marks] Reeall from Question 4 that the number of hours that Dirk works productively on any

given day, denoted W, is uniformly distributed between o and 2.4 hour-s and the number

of hours that Dirk sleeps on any given day, denoted s, is normally distributed with mean 7.2 hours and standard deviation 1.4 hours. suppose now the number of hours that Dirk

works productively and the number of hours that Dirk sleeps. on airy given day, are not independent. (a) 4 marks] 1i Dirk believes that the variant-e of 3W + 23 is equal to 7, ﬁnd the expoeted Value of ws. ‘ Solution:

8‘21 For parts (1)) to (d), assume that P({W > 0.75} n {s > 6}) = 0.55. (b) 3 marks] Find the probability tlistDirk sleeps for more tlianslieurs today. given

that he worked produetively for less than 0.75 hours today. Solution:

0.8163 (c) 3 marks] Find the probability that Dirk sleeps for less than 6 hours today and

works productively for less than 0.75 hours today. Solution:

0.0574