Statistics and Probability Answers

8. In a lottery 200 tickets are sold. Tickets are either red or blue. The winning ticket is chosen at random. a) What is the probability that the winning ticket will be green? b) 79 children and 90 women buy one ticket each. Men buy the rest of the tickets.

Find the probability that a man buys the winning ticket.

2. An ordinary die is rolled once. Find the probability that

i. An even number occurs

ii. A number greater than 4 occurs

1. A card is drawn at random from an ordinary pack of 52 playing cards. Find the probability that the card is a seven.

12. In testing a certain kind of truck tire over rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find the probability that

(a) from 3 to 6 have blowouts;

(b) fewer than 4 have blowouts;

(c) more than 5 have blowouts

6. Two ordinary six-sided dice were tossed. Set up a sample space for this experiment and hence find the probability that

i. Sum of the points on the two dice is 7,

ii. Points on the first die are greater than the points on the second die,

iii. First die shows an even number,

iv. Points on the dice are the same, (i.e. throwing a double),

v. Difference in the outcomes of two dice is 2.

A random sample of 100 recorded deaths in Kenya during the past year showed an average lifespan of 71.8 years with a standard deviation of 8.9 years. Does this seem to indicate that the average lifespan today is greater than 70 years at 0.05level of significance?

Two balls are drawn in succession without replacement from an urn containing 5 white balls and 6 black balls. Let Z be the random variable representing the number of black balls. Construct the probability distribution of the random variable Z.

Possible Outcomes-

Value of the Random Variable Z(Number of Blue Balls)-

State the null and the alternative hypothesis in words and in symbols. State whether the test is directional (one-tailed) or non-directional (two-tailed). If it is directional, tell whether if it is left-tailed or right tailed. 

a.) A teacher wants to know if listening to popular music affects the performance of pupils. A class of 50 grade 1 pupils was used in the experiment. The mean score was 82 and the standard deviation is 5. A previous study revealed that µ = 81 and the standard deviation = 10.  

b.) A farmer believes that using organic fertilizers on his plants will yield greater income. His average income from the past was P300, 000.00 per year.  

c.) The owner of a factory that sells a particular plastic bottled shampoo claims that the average capacity of a bottle of their product is 200 ml.  

Given : n = 6, ∑(x − 18.5) = −3, ∑(y − 50) = 20, ∑(x − 18.5)(y − 50) = −120,

∑(x − 18.5)

2 = 19, ∑(y − 50)

2 = 850 . Calculate coefficient of correlation.

52 well-shuffled playing cards are distributed at random among 4 player's.Find the probability that a hand contain (i) 3 aces (ii) 2 kings and one queen (iii) No cards of diamond (iv) 5 pictured cards.