### Normal Distribution ProblemGiven a normal distribution with a mean (μ) of 104 and a standard deviation (σ) of 20, and given you select a sample of size n = 16, complete parts (a) through (d).**a. What is the probability that X is less than 94?**\[ P(X < 94) = \_\_\_ \](Type an integer or decimal rounded to four decimal places as needed.)**Explanation:**To find the probability that $ X $ is less than 94, you need to calculate the z-score using the formula:\[ z = \frac{X - \mu}{\sigma/\sqrt{n}} \]Where:- $ X $ is the value for which you're finding the probability.- $ \mu $ is the mean.- $ \sigma $ is the standard deviation.- $ n $ is the sample size.Once you have the z-score, use the standard normal distribution table or a calculator to find the corresponding probability.

Refer Standard normal table/Z-table OR use excel formula "=NORM.S.DIST(-2, TRUE)" to find the…

Given a normal distribution with u= 104 and o = 20, and given you select a sample of n= 16, complete parts (a) through (d). a. What is the probability that X is less than 942 PX<94) - (Type an integer or decimal rounded to four decimal places as needed)

Given a normal distribution with u= 104 and o = 20, and given you select a sample of n= 16, complete parts (a) through (d). a. What is the probability that X is less than 942 PX<94) - (Type an integer or decimal rounded to four decimal places as needed)

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Normal Distribution Problem

Given a normal distribution with a mean (μ) of 104 and a standard deviation (σ) of 20, and given you select a sample of size n = 16, complete parts (a) through (d).

**a. What is the probability that X is less than 94?**

\[ P(X < 94) = \_\_\_ \]

(Type an integer or decimal rounded to four decimal places as needed.)

**Explanation:**

To find the probability that $ X $ is less than 94, you need to calculate the z-score using the formula:

\[ z = \frac{X - \mu}{\sigma/\sqrt{n}} \]

Where:
- $ X $ is the value for which you're finding the probability.
- $ \mu $ is the mean.
- $ \sigma $ is the standard deviation.
- $ n $ is the sample size.

Once you have the z-score, use the standard normal distribution table or a calculator to find the corresponding probability.

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