Three firms carry inventories that differ in size. Firm A's inventory contains 2,000 items, firm B's inventory contains 5,000 items, and firm C's inventory contains 10,000 items. The population standard deviation for the cost of the items in each firm's inventory is a = 121. A statistical consultant recommends that each firm take a sample of 50 items from its inventory to provide statistically valid estimates of the average cost per item. Managers of the small firm state that because it has the smallest population, it should be able to make the estimate from a much smaller sample than that required by the larger firms. However, the consultant states that to obtain the same standard error and thus the same precision in the sample results, all firms should use the same sample size regardless of population size. (a) Using the finite population correction factor, compute the standard error for each of the three firms given a sample of size 50. (Round your answers to two decimal places.) firm A firm B firm C (b) What is the probability that for each firm the sample mean x will be within 125 of the population mean u? (Round your answers to four decimal places.) firm A firm B firm C
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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