Statistics and Probability Answers

A population consists of four numbers 2, 3, 4, 5. Consider all possible distinct

samples of size two with replacement. Find (i) the population mean (ii) the

population standard deviation (iii) the sampling distribution of means (iv)

standard deviation of the sampling distribution of means

The literacy rate for a nation measures the proportion of people age 15 and over that can read and write.The literacy rate in Afghanistan is 28.1%.Suppose you choose 15 people in Afghanistan at random.Let X=Number of people who are literate.

i)Determine the probability distribution of X hence write down the mean and standard deviation of X

ii)is it more likely that 3 people or 4 people are literate?

iii)Find the probability that more than five people in the sample are literate

iv)Suppose you sample the Afghans until you find a literate person ,what is the probability that you will sample 4 people before getting one who is literate?

1)    A dice is tossed 120 times with the following results

No. turned up

1

2

3

4

5

6

Frequency

30

25

18

10

22

15

Test the hypothesis that the dice is unbiased (X² = 11.7). Calculate the frequency observed for Chi Square distribution.

The length of the song that you listen to. What types of graphs to use. Scatterplot. Circle graph. Histogram. Bar graph

The heights of ten children selected at random from a given locality had a mean 63.2cm and variance 6.25cm. Test at 5% level of significance, the hypothesis that the children of the given locality are on average less than 65 cm. given for 9 degrees of freedom P(t>1.83)=0.05

Wait Times at Car Repair Garages. The Car Repair Ratings website provides consumer reviews and ratings for garages in the United States and Canada. The time customers wait for service to be completed is one of the categories rated. The following table provides a summary of the wait-time ratings (1 = Slow/Delays; 10 = Quick/On Time) for 80 randomly selected garages located in the province of Ontario, Canada. (15 points) Wait-Time Rating 1 2 3 Number of Garages 12 4 5 6 7 8 9 10 4 6 4 10 4 8 10 10 12 NO a. Develop a probability distribution for x = wait-time rating. b. Any garage that receives a wait-time rating of at least 9 is considered to provide outstanding service. If a consumer randomly selects one of the 80 garages for their next car service, what is the probability the garage selected will provide outstanding wait-time service? c. What is the expected value and variance for x?

A consumer organisation wants to obtain information about u, the mean number of drawing pins in the boxes of a certain brand which, according to the label, should contain 100 pins. In nine randomly chosen boxes this organisation finds the following numbers of drawing pins:

90 94 88 92 90 86 94 90 86

a)(i) Test whether u < 100. Take as level of significance a= 0:05.

(ii) Which assumption do you need?

b)If the true value of u is 101, what type of error did you make in part (a)?

c)(i) Determine a 90% confidence interval for u.

(ii) Is it likely that u= 101?