calculate the probability of selecting a sample with a mean of 29.85 grams or less to be ____.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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As the plant operations manager for Oxford Biotech, you are responsible for monitoring the amount of product placed in each carton. To be consistent with package labeling, cartons should contain a mean of 30 grams of product. Thousands of cartons are produced during a shift, and weighing every single carton was determined to be too time-consuming, costly, and inefficient. Instead, a random sample of cartons is selected. Based on your analysis of the sample, you had to decide whether to maintain, alter, or shut down the process.

Using the concept of the sampling distribution of the mean, you are able to determine probabilities that such a sample mean could have been randomly selected from a population with mean of 30 grams. Specifically, if a sample size of n = 20 is selected from a population with mean of 30 grams and standard deviation of 0.60, you calculate the probability of selecting a sample with a mean of 29.85 grams or less to be ____.  

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