Question

In: Statistics and Probability

For a normal population with ? = 70 and ? = 12, find the following. (a)...

For a normal population with ? = 70 and ? = 12, find the following.

(a) What is the probability of obtaining a sample mean greater than 73 for a sample of n = 36 scores?

(b) What is the probability of obtaining a sample mean greater than 73 for a sample of n = 9 scores?

What type of problem is this?

What am I solving (looking) for?

Solutions

Expert Solution

a) given ? = 70 and ? = 12

probability of obtaining a sample mean

P( x>73) = x - ? / ? / sqrt(n)

             = 73-70 / 12 / sqrt(36)

             = 3/ 12/ 6

            = 3/2

             =1.5

P( x > 1.5) = 1? P( Z<1.5 )=1?0.9332=0.0668

b)

P( x>73) = x - ? / ? / sqrt(n)

             = 73-70 / 12 / sqrt(9)

             = 3/ 12/ 3

            = 3/4

             =0.75

P( x > 0.75) = 1? P( Z< 0.75 ) = 1?0.7734 = 0.2266

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The following data were drawn from a normal population. Find a 98.6% confidence interval for the...
The following data were drawn from a normal population. Find a 98.6% confidence interval for the mean. 15 18 18 22 20 9 17 9 11 16 UCL = LCL =
The following data were drawn from a normal population. Find a 98.4% confidence interval for the...
The following data were drawn from a normal population. Find a 98.4% confidence interval for the mean. 7 21 20 8 14 12 18 14 9 23
The expected mean of a normal population is 100, and its standard deviation is 12. A...
The expected mean of a normal population is 100, and its standard deviation is 12. A sample of 49 measurements gives a sample mean of 96. Using the α = 0.01 level of significance a test is to be made to decide between “population mean is 100” or “population mean is different than 100.” a) State null H0. b) What conclusion can be drawn at the given level of significance α = 0.01. c) What conclusion can be drawn if...
. The expected mean of a normal population is 100, and its standard deviation is 12....
. The expected mean of a normal population is 100, and its standard deviation is 12. A sample of 49 measurements gives a sample mean of 96. Using the α = 0.01 level of significance a test is to be made to decide between “population mean is 100” or “population mean is different than 100.” a) State null H0. b) What conclusion can be drawn at the given level of significance α = 0.01. c) What conclusion can be drawn...
. The expected mean of a normal population is 100, and its standard deviation is 12....
. The expected mean of a normal population is 100, and its standard deviation is 12. A sample of 49 measurements gives a sample mean of 96. Using the α = 0.01 level of significance a test is to be made to decide between “population mean is 100” or “population mean is different than 100.” a) State null H0. b) What conclusion can be drawn at the given level of significance α = 0.01. c) What conclusion can be drawn...
The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 6,...
The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 6, 5. a. What is the point estimate of the population mean? b. What is the point estimate of the population standard deviation (to 2 decimals)? c. With 95% confidence, what is the margin of error for the estimation of the population mean (to 1 decimal)? d. What is the 95% confidence interval for the population mean (to 1 decimal)? ( ,  )
The following eight observations were drawn from a normal population whose variance is 100: 12 8...
The following eight observations were drawn from a normal population whose variance is 100: 12 8 22 15 30 6 29 58 Part A What is the standard error of the sample mean, based on the known population variance? Give your answer to two decimal places in the form x.xx Standard error: Part B Find the lower and upper limits of a 90% confidence interval for the population mean. Give your answer to two decimal places in the form xx.xx...
The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 7,...
The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 7, 4. a. What is the point estimate of the population mean? b. What is the point estimate of the population standard deviation (to 2 decimals)? c. With 95% confidence, what is the margin of error for the estimation of the population mean (to 1 decimal)? d. What is the 95% confidence interval for the population mean (to 1 decimal)? ( , )
A sample of n = 4 individuals is selected from a normal population with μ = 70 and σ = 10.
  3) A sample of n = 4 individuals is selected from a normal population with μ = 70 and σ = 10. A treatment is administered to the individuals in the sample, and after the treatment, the sample mean is found to be 75.      a) On the basis of the sample data, can you conclude that the treatment has a significant effect?           (Use a two-tailed test with α = .05).      b) Suppose that the sample consisted...
A. For a population with μ = 62 and σ = 12, find the X value...
A. For a population with μ = 62 and σ = 12, find the X value that corresponds to each of the following z-scores. z = −0.25     z = −1.50     z = 0.50 z = 2.00 B. A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT