**Probability and the Normal Distribution**Assume the random variable \( X \) is normally distributed with a mean \( \mu = 50 \) and a standard deviation \( \sigma = 7 \). Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.\[ P(34 < X < 60) \]Click the icon to view a table of areas under the normal curve.**Question:**Which of the following normal curves corresponds to \( P(34 < X < 60) \)?- **Option A:** Shows a normal distribution curve with the area between 34 and 60 shaded. The shaded region starts at the left tail (at 34) and extends to 60.- **Option B:** Displays a normal distribution curve with a small area shaded to the right of 60, not corresponding to the desired probability range.- **Option C:** Illustrates a normal distribution curve with the area between 34 and 60 shaded, accurately reflecting the probability from 34 to 60 under the normal distribution.To solve for the correct region under the curve, identify the area between the two specified points (34 and 60) on the normal distribution curve with the mean and standard deviation provided. ### Standard Normal Distribution TableThis table provides the cumulative probabilities of the standard normal distribution, often referred to as Z-table or Z-score table.#### Understanding the Table- **Rows and Columns**: The table is divided into rows and columns. The rows represent the Z-score value up to one decimal place. The column headers range from .00 to .09 and represent the second decimal place of the Z-score.- **Z-score**: This is a measure of how many standard deviations an element is from the mean. It is represented by the variable \( z \).#### Reading the TableTo find the cumulative probability for a given Z-score:1. **Find the Row**: Identify the row for the first decimal place of the Z-score. 2. **Find the Column**: Identify the column for the second decimal place of the Z-score.3. **Locate the Probability**: The cell where the row and column intersect gives the cumulative probability.#### Example- If you need the cumulative probability for a Z-score of 1.23, go to the row labeled \( 1.2 \) and the column labeled \( .03 \). The value in this cell is the cumulative probability.#### Parts of the Table- **Negative Z-scores**: Values from -3.4 to almost zero. Probabilities less than 0.5. - **Positive Z-scores**: Values from 0 to 3.4. Probabilities greater than 0.5, approaching 1.This standard normal distribution table is an essential tool in statistics for finding probabilities and percentiles related to the normal distribution.

Answered: P(34 | bartleby

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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Sketch a standard normal curve and shade the area that lies to the left of a. -1.15 , b. 0.6 , c. 0 , and d. 4.2 . Then determine the area under the standard normal curve that lies in the area of interest for each part. The area to the left of -1.15 is (Round to four decimal places as needed.) The area to the left of 0.6 is (Round to four decimal places as needed.) The area to the left of 0 is (Round to four decimal places as needed.) The area to the left of 4.2 is (Round to four decimal places as needed.)
P Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Dra a graph and find the bone density test scores that can be used as cutoff values separating the lowest 17% and highest 17%, indicating levels that are too low or too high, respectively. Sketch the region. Choose the correct graph below. O A. OB. ..... OC. Dz "z- The bone density scores are (Use a comma to separate answers as needed. Round to two decimal places as needed.) OD. étv MacBook Pro Next 6.7530.758O. 21 rer website name V & 9 207 30 ) 6 ( | H 99 To
In each part, find the area under the standard normal curve that lies between the specified z-score, sketch a standard normal curve, and shade the area of interest. b. -2 and 2 c. - 3 and 3 a. - 1 and 1 a. Find the area under the standard normal curve that lies between - 1 and 1, sketch a standard normal curve, and shade the area of interest. The area under the standard normal curve that lies between - 1 and 1 is (Type an integer or decimal rounded to four decimal places as needed.)
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