Statistics and Probability Answers

Q1.The following table shows the age distribution of live births in Albany County, New York, for 2000.​

Mother’s Age

Number of Deaths due to Accidents

10-14

7

15-19

258

20-24

585

25-29

841

30-34

981

35-39

526

40-44

99

45-49

4

(a) For the data Calculate Mean, median and Mode.

(b) Which average is most appropriate and why?

(c) Comment on the Shape of the distribution from (a).​

Q2. Calculate the arithmetic mean taking A=8.95 by (i) Short-cut Method and (ii) Coding Method for the following data.

Death Rate

3.5-4.4

4.5-5.4

5.5-6.4

6.5-7.4

7.5-8.4

8.5-9.4

9.5-10.4

10.5-11.4

11.5-12.4

12.5-13.4

13.5-14.4

F

1

4

5

13

12

19

13

10

6

4

1

(a) Calculate the standard deviation σ of the distribution consisting of the integers 1 to 5 inclusive. 
(b) Samples are taken of these integers, with each sample consisting of three different integers (10 samples in all) and a second distribution is formed from the means of these samples. If s is the standard deviation of this second distribution, prove that standard deviation =1(Square room of 6)

A continuous random variable X that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 + x)/27. Find (a) P(X < 4); (b) P(3 ≤ X < 4)

Suppose that 3000 drivers in Wakanda were randomly breath-tested on 21 April

2019 and 116 were above the limit of 0.05 blood- alcohol level. On 15 May

2019, 4000 drivers were tested and 98 were above this level.

1.3.1 What additional information would you require before trying to draw conclusion

from these data? (5)

1.3.2 What factors, other than a real change in driver behaviours, could cause such a

drop in the proportion of above-the-limit drivers. (6)

1.4 A set of data has an interquartile range of 20 and a lower quartile of 6. If the data

is symmetrical, calculate the value of the median.

Given a population of 5000 score with the mean and . How many scores are:

A lottery ticket pays off 300,000,000 pesos is made available for 10,000,000 tickets. Each ticket costs 50 pesos. Supposed the variable X gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only one ticket?

Suppose that on average 2 people in a major city die each year from alien attack. Suppose that each

attack is random and independent.

(a) If X is the number of deaths from alien attack within the next year from a randomly selected

major city, what type of random variable is X?

(b) Use the Poisson approximation to approximate the probability that the next major city you visit

will have at least 3 deaths due to alien attack?

(c) Why do you think a Poisson approximation is used instead of a normal approximation?

A roulette wheel has 38 slots: 18 red, 18 black, and 2 green. The ball ends at one of these at random.

You are a player who plays a large number of games and makes an even bet of Ghc 1 on red in every

game. After n games, what is the probability that you are ahead? Answer this for n = 100 and

n = 1000.