What is the mean of the sampling distribution of ¯xx¯?What is the mean of the sampling distribution of ¯xx¯?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. A population distribution has a normal distribution with μ=192μ=192 and σ=51σ=51. You intend to draw a random sample of size n=25n=25. Determine the mean and standard deviation of the sampling distribution of ¯xx¯. Round solutions to four decimal places, if necessary

What is the mean of the sampling distribution of ¯xx¯?

What is the mean of the sampling distribution of ¯xx¯?

2. A population of values has a normal distribution with μ=175.6μ=175.6 and σ=6.4σ=6.4. You intend to draw a random sample of size n=34n=34. Determine the mean and standard deviation of the sampling distribution of ¯xx¯. Round solutions to four decimal places, if necessary.

What is the mean of the sampling distribution of ¯xx¯?

What is the standard deviation of the samping distribution of ¯xx¯?

3. Suppose the standard deviation of the weights of all Florida manatees is 33 pounds. Let ¯xx¯ be the mean weight for a sample of a certain number of Florida manatees. What sample size will give the standard deviation of ¯xx¯ equal to 5 pounds?

Round the solution up to the nearest whole number, if necessary.n=?

4. Suppose the standard deviation of the ages of all Florida panthers is 14.4 years. Let ¯xx¯ be the mean age for a sample of a certain number of Florida panthers. What sample size will give the standard deviation of ¯xx¯ equal to 1.3 years?

Round the solution up to the nearest whole number, if necessary.n=?

5. A population distribution is normally distributed with μ=150μ=150 and σ=27σ=27. Use this information to determine the following two probabilities. Round solutions to four decimal places, if necessary.

Find the probability that a single randomly selected observation is less than than 145.

Find the probability that a sample of 109 randomly selected observations has a mean less than than 145.

6. The distribution of all registered nurses' salaries on the Treasure Coast is known to be normally distributed with a mean of $58,45058,450 and a standard deviation of $725725. Use this information to determine the following two probabilities. Round solutions to four decimal places, if necessary.

Find the probability that a single randomly selected nurse's salary is less than $58,477.

Find the probability that a random sample of 4646 nurses have a mean salary less than $58,477.

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