Question

In: Statistics and Probability

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.

D. No, the standard normal distribution could be used only for the sample size n = 36.

Solutions

Expert Solution

Solution :

Given that,

mean = = 66

standard deviation = = 5.5

n = 16

The sampling distribution of mean and standard deviation is ,

= 66 and

= / n = 5.5 / 16 = 5.5 / 4 = 1.375

n = 36

The sampling distribution of mean and standard deviation is ,

= 66 and

= / n = 5.5 / 36 = 5.5 / 6 = 0.9167

A. Yes, both the sample means will have a normal distribution.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

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...
A random sample is drawn from a population with mean μ = 74 and standard deviation...
A random sample is drawn from a population with mean μ = 74 and standard deviation σ = 6.2. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 18 and n = 47 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 = 18 will have...
A random sample is drawn from a normally distributed population with mean μ = 33 and...
A random sample is drawn from a normally distributed population with mean μ = 33 and standard deviation σ = 2.1. Use Table 1. a. Are the sampling distributions of the sample mean with n = 41 and n = 82 normally distributed? Yes No b. Can you use the standard normal distribution to calculate the probability that the sample mean is less than 33.6 for both sample sizes? Yes No c. Calculate the above probabilities for both sample sizes....
A random sample is drawn from a normally distributed population with mean μ = 27 and...
A random sample is drawn from a normally distributed population with mean μ = 27 and standard deviation σ = 2.1. [You may find it useful to reference the z table.] a. Are the sampling distribution of the sample mean with n = 35 and n = 70 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 = 35...
A random sample is drawn from a normally distributed population with mean μ = 18 and...
A random sample is drawn from a normally distributed population with mean μ = 18 and standard deviation σ = 2.3. a. Are the sampling distributions of the sample mean with n = 26 and n = 52 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 = 26 will have a normal distribution. No, only the sample mean...
A random sample is drawn from a normally distributed population with mean μ = 19 and...
A random sample is drawn from a normally distributed population with mean μ = 19 and standard deviation σ = 1.8. [You may find it useful to reference the z table.] a. Are the sampling distribution of the sample mean with n = 27 and n = 54 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 = 27...
A random sample is drawn from a normally distributed population with mean μ = 23 and...
A random sample is drawn from a normally distributed population with mean μ = 23 and standard deviation σ = 2.6. [You may find it useful to reference the z table.] a. Are the sampling distribution of the sample mean with n = 31 and n = 62 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 = 31...
A random sample is drawn from a normally distributed population with mean μ = 18 and...
A random sample is drawn from a normally distributed population with mean μ = 18 and standard deviation σ = 2.3. [You may find it useful to reference the z table.] b. Calculate the probabilities that the sample mean is less than 18.6 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) n Probability 26 52
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT