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The mean cost of a five pound bag of shrimp is 50 dollars with a standard deviation of 6 dollars. If a sample of 40 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 51.3 dollars? Round your answer to four decimal places.

The mean cost of a five pound bag of shrimp is 50 dollars with a standard deviation of 6 dollars. If a sample of 40 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 51.3 dollars? Round your answer to four decimal places.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem Statement:** The mean cost of a five-pound bag of shrimp is $50, with a standard deviation of $6. If a sample of 40 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than $51.3? Round your answer to four decimal places. **Answer Box:** - [How to enter your answer (opens in new window)](link) **Tools Provided:** - Tables - Keypad - Keyboard Shortcuts
Transcribed Image Text:**Problem Statement:** The mean cost of a five-pound bag of shrimp is $50, with a standard deviation of $6. If a sample of 40 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than $51.3? Round your answer to four decimal places. **Answer Box:** - [How to enter your answer (opens in new window)](link) **Tools Provided:** - Tables - Keypad - Keyboard Shortcuts
This table is a Standard Normal Distribution table, which provides values representing the area to the left of a given Z-score. The Z-score is represented in the leftmost column (Z) with decimal precision to the first digit. Across the top, there are columns labeled from .00 to .09, which further refine the Z-score to two decimal places. ### Explanation: - **Z-Score column**: Each row begins with a Z-score, from -3.9 to 0.0. This score represents standard deviations away from the mean in a standard normal distribution. - **Columns .00 to .09**: These headers represent the hundredths place in the Z-score. For example, a Z-score of -1.38 would require looking at the row labeled -1.3 and then across the column under .08. - **Values**: Every intersection of a row and column gives the cumulative probability from the far left up to that Z-score. For example, a Z-score of -1.38 gives a cumulative probability of 0.08379, meaning approximately 8.379% of the data falls to the left of this value in a standard normal distribution. ### Highlighted Values: - Specific Z-scores and their respective cumulative areas, such as -1.4 with an area of 0.08076 and -1.3 with an area of 0.08379, are marked for quicker reference, signifying important or commonly referenced values. This table is essential in statistics for converting Z-scores to percentiles in a standard normal distribution, helping to determine probabilities and areas under the curve.
Transcribed Image Text:This table is a Standard Normal Distribution table, which provides values representing the area to the left of a given Z-score. The Z-score is represented in the leftmost column (Z) with decimal precision to the first digit. Across the top, there are columns labeled from .00 to .09, which further refine the Z-score to two decimal places. ### Explanation: - **Z-Score column**: Each row begins with a Z-score, from -3.9 to 0.0. This score represents standard deviations away from the mean in a standard normal distribution. - **Columns .00 to .09**: These headers represent the hundredths place in the Z-score. For example, a Z-score of -1.38 would require looking at the row labeled -1.3 and then across the column under .08. - **Values**: Every intersection of a row and column gives the cumulative probability from the far left up to that Z-score. For example, a Z-score of -1.38 gives a cumulative probability of 0.08379, meaning approximately 8.379% of the data falls to the left of this value in a standard normal distribution. ### Highlighted Values: - Specific Z-scores and their respective cumulative areas, such as -1.4 with an area of 0.08076 and -1.3 with an area of 0.08379, are marked for quicker reference, signifying important or commonly referenced values. This table is essential in statistics for converting Z-scores to percentiles in a standard normal distribution, helping to determine probabilities and areas under the curve.
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