Statistics and Probability Answers

If there is an increase in capital investment next year, the probability that the price of structural steel will increase is 0.90. If there is no increase in such investment, the probability of an increase is 0.40. Overall, we estimate that there is 60% chance that the capital investment will increase next year.

i) What is the overall probability of an increase in structural steel prices next year?

ii) Suppose that during the next year structural steel prices in fact increase what is the probability that there was an increase in capital investment?

Suppose you and your three friends have two dice each. 

1. When you roll your dice, what are the chances you get a pair? (example (1:1), (2:2))
2. When 2 dice are thrown, what is the probability of the sum being 9? (example (4:5)
3. When everyone rolls, what are the chances that there is at least one 6?

What will happen to the mean of the sampling distribution of the sample means if the sample size increases?

 In sampling distribution of the sample means, what can you observe about the population mean and the mean of the sampling distribution?

Here are the results of a cross-tabulation table drawn from sample data. Two variables were measured in this study, age and concern about rising inequality in US society.

Very Somewhat Not at all

concerned concerned concerned

Over 30 10 35 55

30 or younger 60 25 15

n =

1. In our study of feelings about inequality in the US ______________% of the sample is over 30 and ____________ % is 30 or younger.
2. According to our study____________ % of respondents are very concerned about rising inequality in the US, while __________ % of people we surveyed are not at all concerned.
3. Importantly, we note that ___________% of respondents who are 30 or younger are very concerned with rising inequality, while only __________% of respondents over 30 feel this way about the issue.

From a box containing 2 apples, 2 peaches and 2 oranges, 3 fruits are drawn at

random. Let P be a random variable representing the number of oranges that occur. Construct a probability distribution.

1.     A random sample consisting of 5 employees of a certain company who drive cars were selected to see if alcohol affects actual driving. Each driver’s reaction time was tested in a laboratory before and after drinking beer. The following are results:

Employee

Before

After

Mokua

0.68

0.73

Njoroge

0.64

0.62

Ethan

0.68

0.66

Marwa

0.82

0.92

Kibet

0.58

0.68

Test whether alcohol affects reaction time (10 Marks)

1.     In a psychological experiment a researcher has six different groups with the following number of respondents: 25,30,18,27,28,22. Find

i) Mean (1 mks)

ii) Variance (3 mks)

iii Standard deviation (1 mks)

The probability that a child went to his tutor will have a lecture is 0.6; the probability that a child who had a lecture will also have a assignment is 0.3; and the probability that a child who has had a lecture and an assignment will also have a quiz is 0.1. What is the probability that a child visiting his tutor will have a lecture, an assignment, and a quiz?

The probabilities of a machine manufacturing 0, 1, 2, 3, 4, or 5defective parts in one day are 0.75, 0.17, 0.04, 0.025, 0.01, and 0.005, respectively. The computed variance is _____ and standard deviation is _____ of the distribution.

NOTE: Round off your answer to the nearest hundredths