**Problem Statement:**Randomly sample 256 items from a population where individuals have a normal distribution with a mean of 120 and a standard deviation of 160. Find the following probability rounded to 4 decimal places.**Graph/Diagram Explanation:**The diagram is a normal distribution curve representing the sampling distribution of the sample mean. It has a symmetric bell shape centered at the population mean of 120. The x-axis ranges from 80 to 160 with increments of 10. Below the x-axis, the corresponding z-scores are marked:- z = -4 at x = 80- z = -2 at x = 100- z = 0 at x = 120 (mean)- z = 2 at x = 140- z = 4 at x = 160The shaded area under the curve represents the probability of the sample mean falling between the given range.**Probability Expression:**\[ P(110.5 < \bar{x} < 143.2) = \](Use this space to calculate or provide the probability value using statistical methods or tools.)

Sample size(n)=256mean()=120Standard deviation()=160

Answered: Randomly sample 256 items from a…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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Randomly sample 256 items from a population where individuals have a normal distribution with a mean of 120 and a standard deviation of 160, find the following probability rounded to 4 decimal places. 80 z = -4 90 100 z = -2 110 120 P (110.5 < < 143.2) z = 0 130 140 z = 2 150 160 z = 4