Statistics and Probability Answers

 A population consists of six scores: 11, 13, 15, 16, 17, and 19. If

a sampling distribution of size 3 is drawn from the population, what is the standard

error of the mean of the sampling distribution? complete solution

 A population has mean and standard deviation of 20 and 3.15,

respectively. What is the standard error of the mean of the sampling

distribution in a sample size of 5? complete solution

4. Mrs. Dela Cruz gave a 50-item test to her 115 Grade 12 students.

The result of the exam shows an average score of 36 with a standard deviation

of 2.7. Suppose Mrs. Dela Cruz repeatedly took 33 samples and calculated the

sample mean from each sample. complete solution

4.1. Find the mean of the sample means.

4.2. Compute for the standard error of the

sample mean.

4.3. Determine the shape of the sampling

distribution of the sample mean.

Compute for the standard error of the mean given the population variance and the sample size. Show your complete solutions.3.1. 𝜎" = 20.50; 𝑛 = 33.2. 𝜎" = 13.18; 𝑛 = 5 

A set of data consists of values 10, 12, 14, 16, and 18. Using a

sample size of 3 without replacement, illustrate the Central Limit Theorem by

showing that the histogram of the sampling distribution of the sample mean

resembles a bell curve. complete solution

Sheldon owns a mango farm and the weight of his mangoes are

normally distributed with an average weight of 200 grams and a standard

deviation of 15 grams. If there are 800 mangoes in the farm, what is the mean

and standard deviation of the sample mean weights of 50 mangoes?

When trying to determine if there is a relationship between two variables many statisticians utilize a?

 A social psychologist is interested in gender differences in the sociability of teenagers. Using the number of good friends as an indicator of sociability, the researcher found that females had on average 5.9 close friends (s=3.1; n=44) and males had on average 4.8 close friends (s=2.6; n=35). Is the difference in the sociability between males and

females statistically significant? Set alpha to 0.02 find Null and research hypothesis 1 or two tailed? Find Critical value? find test statistic?

In a number series representing X as 3, 6, 8. 7, 9, 3, 4, 6, 6, 8, 6, 4, 3, 7, 4, kindly show clear solutions on the following:

a)      what number is the most frequently appearing? how do you call the number?

b)     How many X values are there?

c)      what is ΣX equal to?

d)     what is the n equal to in the number series?

e)      show the longhand of ΣX/n and what is that particularly equal to?

f)       what is the lowest equivalent of n in the above number series if X is equal to each of the values in the series?

g)     what is the highest equivalent of n in the above number series if X is equal to each of the values in the series?

h)     what is the midpoint of this series?

i)       what is ΣX² equal to?

 Let X be a discrete random variable with the following PMF pX(k) = 0.2 for k = 0 0.2 for k = 1 0.3 for k = 2 0.3 for k = 3 0 otherwise (i) Let Y = X(X − 1)(X − 2), find pY (y). (ii) Find E[Y ] and V AR[Y ].