(a)A recent survey asked a sample of 50 persons “How often do you attend religious services?” Of those sampled, 30 were women and 20 were men. Of the women surveyed:
70 percent reported that they attend religious services regularly
30 percent reported that they do not attend religious services regularly
Of the men surveyed:
20 percent said they attend religious services regularly
80 percent reported that they do not attend religious services regularly
(i) Use the information above to complete the following contingency table:
|
Attend religious services regularly
|
Do not attend religious services regularly
|
Total
|
Women
|
|
|
30
|
Men
|
|
|
20
|
Total
|
|
|
50
|
(ii) Using your answer to part (a), calculate the probability that a randomly selected respondent who attends religious services regularly is a male.
(iii) Are the events ‘attend religious services regularly’ and ‘respondent is male’ independent? Give reasons for your answer.
(iv) Are the events ‘attend religious services regularly’ and ‘respondent is male’ mutually exclusive? Give reasons for your answer.
Ms Greenaway sells mangoes at a roundabout in her town. On any given day, the probability of Ms Greenaway selling 0 mangoes is 0.1, the probability of Ms Greenaway selling 1 mango is 0.7 and the probability of Ms Greenaway selling 2 mangoes is 0.2.
(v) Construct the probability distribution table for Ms Greenaway’s mango sales.
(vi) Calculate Ms Greenaway’s expected daily mango sales
and
the standard deviation of Ms Greenaway’s daily mango sales.