Statistics and Probability Answers

A. Find the mean (𝝁𝑿), variance (𝝈 𝑿

𝟐) and standard deviation (𝝈𝑿) of the sampling distribution of the means given the sample size, and the means and variances of the population. Sample size n were randomly selected from the population.

1. 𝑛 = 3

𝜇 = 6

𝜎² = 2.4

Mean:

Variance:

Standard Deviation:

2. 𝑛 = 25

𝜇 = 20

𝜎² = 5.5

Mean:

Variance:

Standard Deviation:

2. Average Senior High School annual cost of tuition fee for all private schools last year

was Php43,700. A random sample of costs this year for 45 private schools indicated

that the sample mean was Php45,800 and a sample standard deviation was Php5,600.

At 0.01 level of significance, is there sufficient evidence to conclude that the cost

increased?

A population consist of three numbers 3,4,8.Consider all possible samples of size 2 which can be drawn with replacement from the population.Find the following population mean, population variance, population standard deviation

Given the population 3, 5, 8, 9, and 10. Suppose samples of size 4 are drawn from this

population.

1. What is the mean (μ) and standard deviation (σ) of the population?

2. How many different samples of size n = 4 can be drawn from the population? List them with their corresponding means.

Sample Mean

1.

2.

3.

4.

5.

3. Construct the sampling distribution of the sample means.

Sample Mean𝐗̅ Frequency Probability(𝐗̅)

1.

2.

3.

4.

5.

6.

4. What is the mean (μX̅) of the sampling distribution of the sample means? Compare this to the mean of the population.

5. What is the standard deviation (σX̅) of the sampling distribution of the sample means? Compare this to the standard deviation of the population.

1. Samples of eight cards are drawn at random from a population of nine cards numbered from 1 to 9.

a. How many possible samples can be drawn?

b. Construct the sampling distribution of sample means.

A molding machine prepares a certain kind of car spare part with a target diameter 𝜇 =

40.265 millimeters. The machine has some variability, so the standard deviation of the

diameters is 𝜎 = 0.004 millimeters. A sample of 6 spare parts is inspected each hour for

process control purposes and records are kept of the sample mean diameter. What will be

the mean and standard deviation of the numbers recorded?

a nutritionist claims that her developed bread is fortified with vitamin b. is it one-tailed or two-tailed?

Activity #1

Suppose that a coin is to be tossed five times, and let X represent the number of tails that occur. Based on the problem, observe, analyze, and answer the following questions:

How many outcomes are possible?

Construct a table showing the number of tails appear in each outcome and assign this number to this outcome. What is the value of the random variable X?

> Illustrate a probability distribution. What is the probability value P(X) to each value of the random variable? (Use table)

What is the sum of the probabilities of all values of the random variable?

Suppose that a coin is to be tossed five times, and let X represent the number of tails that occur. Based on the problem, observe, analyze, and answer the following questions:

> Construct a table showing the number of tails appear in each outcome and assign this number to this outcome. What is the value of the random variable X?