Statistics and Probability Answers

3. Suppose that X has a discrete uniform distribution on the integers 0 through 9.

Determine the mean, variance, and standard deviation of the random variable Y = 5X

and compare to the corresponding results for X.

Seven students went on a diet in an attempt to lose weight, with two of them losing weight while all the others added weight. Is the diet is an effective way to losing weight α=1% (5mks)

2. A fire-detection device uses three-temperature-sensitive cells acting independently of

one another in such a manner that any one or more can activate the alarm. Each cell has

a probability p = 0.8 of activating the alarm when the temperature reaches 100° or

higher. Let X represent the number of cells activating the alarm when the temperature

reaches 100°. Find:

a) the probability distribution of X;

b) the expected value; and

c) the variance for the random variable X.

A random sample of size 36 was taken from a population distributed as Nμ,3.92.The value of the sample x was 15.6. i. Find a 90% confidence interval for μ. (5mks)

It is believed that value of μ is 17. Use your confidence interval to comment on this belief.(2mks)

Which is the upper 10%of the normal curve

Dan works in an insurance company. Last January, he was able to insure 2 persons. Last February, he was able to insure 3 persons. Last March, he was able to insure 5 persons. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a. List down the 9 different possible samples. b. Find the mean of each sample. c. Find the mean of the sampling distribution of means. d. Identify the probability of each sample. e. Find the population mean. f. Compare the population mean with the mean of the sampling distribution of means.

Colombo City typically has rained on about 16% of days in November.

a. What is the probability that it will rain on about 16% of days in November?

b. What is the mean number of days with rain in November?

c. What is the variance and standard deviation of the number of days with rain

in November?

Susan and Thomas play a game using two 10p coins. The coins are tossed and

Susan records her score using the random variable S and Thomas records his

score using the random variable T. After a large number of tosses they compare

their scores.

Comment on any likely differences and similarities.

Two fair cubical dice are thrown: one is red and one is blue. The random variable

M represents the score on the red die minus the score on the blue die.

a. Find the distribution of M.

b. Write down E(M).

c. Find Var (M)

Why normal curve is useful in problem solving. Give a real life situation as your own example?