# distribution of sample means, deviation, sample size, random selection

2. Describe the distribution of sample means (shape, expected value, standard error) for samples n= 36 selected from a population with a mean of µ =100 and a standard deviation of Ï? = 12.

6. For a population with a mean of µ =50 and a standard deviation of Ï? = 10, how large a sample mean (M) and the population mean for:

a. sample of n= 4 scores

b. a sample of n = 16 scores

c. a sample of n =25 scores

10. For a population with a mean of µ = 60 and a standard deviation of Ï? = 24, find the z-score corresponding to each of the following samples.

a. M =63 for a sample of n= 16 scores

b. M = 63 for a sample of n= 36 scores

c. M =63 for a sample of n= 64 scores

14. The population of IQ forms a normal distribution with a mean of µ =100 and a standard deviation of Ï? = 15. What is the probability of obtaining a sample of obtaining a sample mean greater than M =105,

a. for a random sample of n= 9 people?

b. for a random sample of n=36 people?

18. The population of SAT scores forms a normal distribution with a mean of µ =500 and a standard deviation of Ï? =100. If the average SAT score calculated for a sample of n = 25 students,

a. What is the probability that the sample mean will be greater than M= 510. In symbols, what is p (M >520?

b. What is the probability that the sample mean will be greater than M = 520. In symbols, what is p (M>520?

c. What is the probability that the sample mean will be between M =510 and M = 520? In symbols, what is p (510 < M < 520?

20. A normal shaped distribution has µ =80 = and Ï? = 15

b. What are the z-score values that form the boundaries for the middle 95% of the distribution of samples means?

c. Compute the z-scores for M =89 for a sample of n=25 scores. In this sample mean in the middle 95% of the distribution?

22. People are selected to serve on juries by randomly picking names from the list of registered voter The average age for registered voters in the county is µ = 39.7 years with a standard deviation of Ï? = 12.4. A statisticians randomly selects a sample of n= 16 people who people who are currently serving on juries. He average age for the individuals in the sample is M = 48. 9 years.

a. How likely is to obtain a random ample of n= 16 jurors with an average age greater tan or equal to 48.9?

b. Is it reasonable to conclude that this set of n = 16 people is not representative random sample of registered voters?

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#### Solution Preview

See the attached file.

2. Let be the sample mean of sample of size selected from a population with mean = 100 and standard deviation = 12. Since the sample size n is large (note that if n is greater than 30, it is considered as a large sample) follows normal distribution with mean = = 100 and standard deviation = . Thus we have

Shape of the distribution = Normal ( Bell shaped)

Expected value = Mean = 100

Standard Error = 2 (standard deviation of the statistic is known as standard error)

6. Given the population mean = 50 and standard deviation = 10. Suppose M denote the sample mean of a sample of size n taken from this population. Then we know follows standard normal distribution. Therefore we have the following probabilities

This means, the maximum difference between the sample mean and population mean with probability 0.90 is , the maximum difference between the sample mean and population ...

#### Solution Summary

A distribution of sample means, deviation, and sample sizes are examined.