Question

1) Which of the following numbers is most likely to represent the correlation between a 25 year old person’s income and their spending on entertainment?

a)–1 b) –0.6 c) 0 d)0.6 e) 1

2) A club prefers when bands start their sets on time. The probability that a band performing there starts on time is 35%. The probability that a band is invited back there is 60%. What is the probability that a band performing there starts on time and is invited back to perform there again?

a) exactly 5% b) at least 5% and less than 21% c) exactly 21% d) more than 21% and at most 35% e) exactly 35% f) more than 35%

3) A bar band gets an average of 8 gigs per month, with a standard deviation of 3. If you wish to use the Z distribution calculator to determine how the probability that the band gets no more than 6 gigs this month, you should enter the following

a) above 7.5 b) above 8 c) above 8.5 d) below 7.5 e) below 8 f) below 8.5

Answer 1

1) The number, most likely to represent the correlation between a 25 year old person’s income and their spending on entertainment would be positive, to start with; since, the expenditure and income are established to be two positively correlated variables. This rules out option a),b) and c). Among option d) and e), it is known that there are several other factors that influence the spending pattern of a person, which prevents the proportional spending of income on Entertainment alone. Hence, a practical correlation value between the two variables would be d) 0.6.

2)

Let A = Event that the band performs on time. B =  Event that the band is invited back. It is given that event B is dependent on event A.

Given: P(A) = 0.35, P(B|A) = 0.60 (Band is invited again if it performs on time) To find: P(AB) = ?

By definition of Conditional Probability,

= 0.21

Correct option would be c) exactly 21%

3) A bar band gets an average of 8 gigs per month, with a standard deviation of 3. If you wish to use the Z distribution calculator to determine how the probability that the band gets no more than 6 gigs this month, you should enter the following:

Given:

If , by definition of standard Z score:

= ?

Hence, the correct option among the given, would be d) below 7.5

Otherwise, Entering the value 6:

From Standard normal table,

= 0.25143

  

a) above 7.5 b) above 8 c) above 8.5 d) below 7.5 e) below 8 f) below 8.5