Question

In: Statistics and Probability

A random sample is selected from a population with a μ = 145 and a standard...

A random sample is selected from a population with a μ = 145 and a standard deviation of σ = 18. Determine the mean and standard deviation of the sampling distribution (round to 3 decimal places).

a. n = 14

Mean:

Standard deviation:

b. n = 26

Mean:

Standard deviation:

c. n = 37

Mean:

Standard deviation:

d. n = 56

Mean:

Standard deviation:

e. n = 115

Mean:

Standard deviation:

Solutions

Expert Solution

Solution :

Given that,

mean = = 145

standard deviation = = 18

a)

n = 14

mean :

= = 145

standard deviation :

= / n = 18 / 14 = 4.811

b)

n = 26

mean :

= = 145

standard deviation :

= / n = 18 / 26 = 3.530

c)

n = 37

mean :

= = 145

standard deviation :

= / n = 18 / 37 = 2.959

d)

n = 56

mean :

= = 145

standard deviation :

= / n = 18 / 56 = 2.405

e)

n = 115

mean :

= = 145

standard deviation :

= / n = 18 / 115 = 1.679

orchestra answered 3 years ago
Next > < Previous

Related Solutions

A random sample is selected from a population with mean μ = 98 and standard deviation...
A random sample is selected from a population with mean μ = 98 and standard deviation σ = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.) (a) n = 8 μ = σ = (b) n = 18 μ = σ = (c) n = 38 μ = σ = (d) n = 55 μ = σ = (f) n = 110...
A random sample is selected from a population with mean μ = 102 and standard deviation...
A random sample is selected from a population with mean μ = 102 and standard deviation σ = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.) (a) n = 11 μ =   σ =   (b) n = 14 μ =   σ =   (c) n = 37 μ =   σ =   (d) n = 65 μ =   σ =   (f) n = 130...
A random sample is drawn from a population with mean μ = 66 and a standard...
A random sample is drawn from a population with mean μ = 66 and a standard deviation σ =5.5. Are the sampling distribution of the sample mean with n = 16 and with n = 36 normally distributed? A. Yes, both the sample means will have a normal distribution. B. No, for both sample sizes, the standard normal distribution could not be used. C. No, the standard normal distribution could be used only for the sample size n = 16....
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ=35 for each of the situations in parts a through d. Calculate a 95​% confidence interval for muμ for each of these situations. a. n=75​, x overbarx=22 b. n=150​,x overbarxequals=110 c. n=90​, x overbarxequals=18 d. n=90​,x overbarxequals=4.69 e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a...
A random sample of n =100 is selected from a normal population with mean μ =...
A random sample of n =100 is selected from a normal population with mean μ = 24 and standard deviation σ = 1.25. Find the probability that  is less than 24.3
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ = 15 for each of the situations in parts a through d. Calculate a 99% confidence interval for μ for each of these situations. a. n = 75, x̄ = 27 b. n = 150, x̄ = 105 c. n = 125, x̄ = 16 d. n = 125, x̄ = 5.37 e. Is the assumption that the underlying population of...
A random sample of n = 25 is selected from a normal population with mean μ...
A random sample of n = 25 is selected from a normal population with mean μ = 101 and standard deviation σ = 13. (a) Find the probability that x exceeds 107. (Round your answer to four decimal places.) (b) Find the probability that the sample mean deviates from the population mean μ = 101 by no more than 2. (Round your answer to four decimal places.)
A random sample is drawn from a population with mean μ = 70 and standard deviation...
A random sample is drawn from a population with mean μ = 70 and standard deviation σ = 5.8. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 17 and n = 43 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 17 will have...
A random sample is drawn from a population with mean μ = 68 and standard deviation...
A random sample is drawn from a population with mean μ = 68 and standard deviation σ = 5.7. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 16 and n = 41 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 16 will have...
A random sample is drawn from a population with mean μ = 72 and standard deviation...
A random sample is drawn from a population with mean μ = 72 and standard deviation σ = 6.0. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 17 and n = 45 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 17 will have...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT