Exam 7: Variation in Repeated Samplessampling Distributions

Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 40 ounces and standard deviation .5 ounce. For a random sample of size n = 16 (a) What are the mean and standard deviation of $\bar{x}$ (b) What is the distribution of $\bar{x}$ Is this distribution exact or approximate? Give your reasoning. (c) Find the probability that $\bar{x}$ lies between 39.75 and 40.25.

Identify the following as either a parameter or a statistic. Sample interquartile range

A large retail store recorded the daily average amount of money spent by its customers in December. The data suggest that the amount of money spent daily can be modeled as a distribution with mean $46 and standard deviation $5.5. If a random sample of size 75 is selected, what is the probability that the sample mean will lie between 44 and 48? Round your answer to four decimal places.

The data suggests than one plausible model, for X, the number of named storms during hurricane season in a year, is a population distribution having mean $\mu$ and standard deviation $\sigma$ . If the standard deviation for a random sample of size 85 is 1.5, what is the standard deviation for a random sample of size 340?

Suppose the number of books consulted by a student last weekend has distribution Let X₁ and X₂ be independent and each have the same distribution as the population. Determine the missing elements in the table for the sampling distribution of .

Suppose the number of evenings that a student studied last weekend has distribution A) The expected value of $\bar{x}$ . B) If the sample size is increased to 48, give the standard deviation of $\bar{x}$ . Round your answer to three decimal places.

A car manufacturer receives, in its facilities, S.U.V's for maintenance. The daily number of rear suspensions they fix per day has probability distribution (a) Find the expected number of rear suspensions fixed per day. (b) What is the approximated distribution of for a sample of size 40?

Suppose the number of passengers in a bus, going from New York City to Washington D.C., has a normal distribution with mean 30.7 passengers and standard deviation 1.1 passengers. If two busses in this route are randomly selected, what is the probability that the average number of passengers is less than 30 passengers? Round your answer to four decimal places.

A random sample of size two was selected, with replacement, from the set of numbers {2, 6, 18}. All possible samples are shown below. A) Evaluate X̄ for each. B) Evaluate S² for each

Extensive data suggest that the number of overtime hours paid by a large company per month can be modeled as a distribution with mean 4.2 and standard deviation 1.1. If P₁ is the probability that the mean of a sample of size 55 lies in the interval (3.6, 4.8) and P₂ is the probability that the mean of a sample of size 110 lies in the interval (3.6, 4.8), then

A car manufacturer receives, in its facilities, S.U.V's for maintenance. The daily number of rear suspensions they fix per day has probability distribution What is the probability distribution of total number of rear suspensions fixed in two days? Assume the number of rear suspensions fixed on different days are independent.

A population has distribution Let X₁ and X₂ be independent and each have the same distribution as the population. (a) Find the expected value and variance of X₁. (b) Determine the missing elements in the table for the sampling distribution of $\bar{X}$ = (X1 + X2) / 2 (c) Find the expected value and variance of $\bar{X}$ . (d) If the sample size is increased to 16, give the mean and variance of $\bar{X}$

The number of calories in a salad sold in the student cafeteria has a normal distribution with mean 145 and standard deviation 6.5. For a sample of size 4, determine the the expected value of X.

Data about the price of a round-trip ticket Atlanta-Barcelona, suggests that a plausible model, for X = price, is a population distribution having mean μ= $689.61 and standard deviation σ =$34.29. A) Calculate the expected value of $\bar{x}$ for a random sample of size 66. B) Calculate the standard deviation of $\bar{x}$ for a random sample of size 66.

The normal approximation is usually adequate when the sample size n is greater than 30.

Take a random sample of size n = 2, without replacement, from {1, 3, 5}. Let $\bar{X}$ = sample range. (a) List all possible samples and the associated value of the sample range. (b) Construct the sampling distribution of the sample range. (c) Obtain the expected value of the sample range using the sampling distribution in Part b.

Suppose the number of coffee drinks ordered by a student yesterday has the distribution Let X₁ and X₂ be independent and each have the same distribution as the population. Find the expected value of $\bar{x}$ .

A random sample of size two was selected, with replacement, from the set of numbers {12, 16, 24}. All possible samples are shown below together with $\bar{x}$ and s². A) Determine the sampling distribution of $\bar{x}$ . B) Determine the sampling distribution of S².

Data associated with gold daily price per gram during the last five years indicates a distribution with mean $32.52 and standard deviation $7.42. What is the standard deviation of $\bar{x}$ when it is based on a random sample of size n = 196?

The number of calories in a salad sold in the student cafeteria has a normal distribution with mean 145 and standard deviation 6.3. For a sample of size 9, determine the A) standard deviation of X. B) Specify the distribution of X.