Statistics and Probability Answers

Question 4 The SA Department of Education in its annual report stated that the tardiness rates (in days) of children differ between the inner city and the suburbs neighborhoods’ schools. Unconvinced with this assertion, you proceed to take random samples of 25 and 20 children in these neighborhoods, respectively. Your findings yielded the following. In the inner city neighborhood the mean and standard error of tardiness were 4 years and 1.8 years. For the suburbs, the tardiness mean rate is 5.2 years while its standard error is 1.2 years. • Which test would you use? (1 mark) • Is it a 1-tail or 2-tail test? (1 mark) • At α = 0.05 is there any significance difference between the variances of the two population? (7 marks). • At α = 0.05 is there any significance difference between the means of the two population? Suppose α = 0.01, would your answer change?

. A basket contains 5 red balls and 11 white balls. If two balls are taken from the

basket one after the other, determine the possible values of the random variable R

representing the number of red balls.

Consider a population with the values (1, 3, 4, 8).

a. Find the population mean.

b. Find the population variance.

c. Find the population standard deviation.

d. Find the mean of the sampling distribution of means.

e. Find the variance of the sampling distribution of means.

f. Find the standard deviation of the sampling distribution of means.

 A guidance counselor at a certain school claims that the students in his school are above average intelligence. A random sample of thirty-five students IQ scores have a mean score of 113.5. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 18. Use a=0.05 (right-tailed). QUESTION: What is the critical value based on the z table: ____ 

An experiment involves rolling a pair of dice once. Let X represent the sum of the numbers on the upturned faces and Y their absolute difference.

a. Construct the probability distribution of X;

b. Construct the probability distribution of Y; and

c. Construct a probability histogram for each probability distribution obtained in (a) and (b).

Mr.A draws a ticket from a box containing 2 bad,10 good and 5 ver good tickets. If Mr.B draw the next ticket, what is his chance of a better performance than Mr .A??

II. Find the expected value, variance, and standard deviation of the following discrete 

probability distributions. (3 items x 15 points) 

1.

T -3 5 7 

P(T) 0.27 0.4 0.33 

2.

X 0 1 2 3 4 

P(x=X) 0.21 0.44 0.06 0.11 0.18 

3.

Y 27 30 14 43 

P(Y=y) 0.3 0.4 0.15 0.15

Consider a population with values (2, 3, 7, 9).

a. Find the population mean.

b. Find the population variance.

c. Find the population standard deviation.

d. Find all possible samples of size 2 which can be drawn with replacement from this 

population. 

e. Find the mean of the sampling distribution of means.

f. Find the variance of the sampling distribution of means.

g. Find the standard deviation of the sampling distribution of means.

Suppose there are two bags with first bag contains 3 white and 2 black balls, second bag contains 2 white and 4 black balls. One ball is transferred from bag I to bag II and then a ball is drawn from the latter. It happens to be white. What is the probability that the transferred ball is white?

Suppose x is a normally distributed random variable with μ=48 and σ=5. Find a value x0 of the random variable x that satisfies the following equations or statements.

a.​ 10% of the values of x are less than x0.

b.​ 1% of the values of x are greater than x0.