Statistics and Probability Answers

Suppose the population consists of the scores of 6 students in a certain examination, as follows: 9, 11, 13, 15, 17 and 19. By using the sampling distribution, estimate the population mean using a random variable of the size n=2.

Suppose the population consists of the scores of 6 students in a certain examination, as follows: 9, 11, 13, 15, 17, and 19 . Byusing the sampling distribution, estimate the population mean using a random variable of the size n=2

Activity IV CHECK WHAT YOU KNOW. Solve the following problems. (2 points each)

1. Given n = 12; = 120 ml;s = 6. The parent population is normally distributed.

Find:

a. The point estimate.

b. The interval estimate of mean.

2. Rochelle wants to know the mean of all entering trainees in a boot camp. The mean age of a

random sample of 25 trainees is 18 years and the standard deviation is 1.3 years. The sample

comes from normally distributed population. Use a = 0.1 to find the following:

a. The point estimate.

b. The error.

c. The interval estimate of the population of the mean.

3.b. The top-selling Amar tire is rated 70,000 KMs, which means nothing. In fact, the distance

the tires can run until they wear out is a normally distributed random variable with a mean

of 82,000 KMs and a standard deviation of 6,400 KMs.

What is the probability that a tire wears out before 70,000 KMs?

What is the probability that a tire lasts more than 100,000 KMs?

Note: You may use Z-table for this.

Z-table link- Normal Table.xls (5 Marks)

A. Consider a population consisting of values (1,3,5).

1. List all the possible samples of size 2 that can be drawn from the population

with replacement.

Observation Sample X (X − μX) (X − μX)²

2. Compute for the mean of the sampling distribution of the sample means.

3. Compute for the variance of the sampling distribution of the sample means.

X f Probability

P(X)

4. Construct the probability histogram of means with replacements when n = 2.

if x is a random variable showing the number of boys in families with 4 children

a. construct a table showing the probability distribution(probability distribution table)

b. find the E(X)

c. Find the Var(X)

Random samples of size 𝑛 = 2 are drawn from a finite population

consisting of the numbers 5,6,7,8, and 9.

a. Find the mean of the population 𝜇.

b. Find the standard deviation of the population 𝜎.

c. Find the mean of the sampling distribution of the sample means 𝜇𝑋̅.

d. Find the standard deviation of the sampling distribution of the sample

means 𝜎𝑋̅.

e. Verify the Central Limit theorem by:

I. Comparing 𝜇 and 𝜇𝑋̅.

II. Comparing 𝜎 and 𝜎𝑋̅.

If a finite population has four elements: 6, 1, 3, 2.

(a) How many different samples of size n = 2 can be selected from this population if you sample without replacement?

(b) List all possible samples of size n = 2.

(c) Compute the sample mean for each of the samples given in part b.

(d) Find the sampling distribution of and draw the histogram.

(e) Compute standard error.

(f) If all four population values are equally likely, calculate the value of the population mean . Do any of the samples listed in part (b) produce a value of exactly equal to mean

A researcher wants to take a random sample of size 40 of a certain population with a mean of 23.5 and a variance of 18.49. What is the approximate standard deviation of sample means?

An emergency service wishes to determine whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data are shown.

Temperature (x) - 25 10 27 30 33

No. of calls (y) - 7 4 8 10 11

a) Find the correlation coefficient r

b) Find the regression equation

c) Graph the regression equation.