### Using Normal Distribution to Solve Problems#### Instructions:Use the normal distribution graph provided to the right to answer the following questions.**Questions:**(a) What percent of the scores are less than 19?(b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21?#### Solution Guide:(a) **Percent of Scores Less Than 19:**- Determine the percentage from the normal distribution.- The result will be rounded to two decimal places.(b) **Number of Scores Greater Than 21:**- Calculate the number based on the normal distribution and the provided number of scores.- The result will be rounded to the nearest whole number as needed.**Graph/Diagram Explanation:**The graph illustrates a normal distribution for standardized test composite scores. It shows:- A bell curve, which represents the distribution of scores.- The mean (average) score, denoted as $ \mu $, is 19.6.- The standard deviation, denoted as $ \sigma $, is 5.2.- Two specific scores, 19 and 21, are marked along the x-axis.The graph visualizes the relationship between the scores and their distribution around the mean.**Form Fields:**(a) The percent of scores that are less than 19 is ___%.(Round to two decimal places as needed.)(b) About ___ scores would be expected to be greater than 21.(Round to the nearest whole number as needed.)

The mean is 19.6 and the standard deviation is 5.2.

Use the normal distribution to the right to answer the questions. Standardized Test Composite Scores (a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? H = 19.6 O = 5.2 19 21 Score (a) The percent of scores that are less than 19 is %. (Round to two decimal places as needed.) (b) About scores would be expected to be greater than 21. (Round to the nearest whole number as needed.)

Use the normal distribution to the right to answer the questions. Standardized Test Composite Scores (a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? H = 19.6 O = 5.2 19 21 Score (a) The percent of scores that are less than 19 is %. (Round to two decimal places as needed.) (b) About scores would be expected to be greater than 21. (Round to the nearest whole number as needed.)

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

### Using Normal Distribution to Solve Problems

#### Instructions:
Use the normal distribution graph provided to the right to answer the following questions.

**Questions:**
(a) What percent of the scores are less than 19?

(b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21?

#### Solution Guide:
(a) **Percent of Scores Less Than 19:**
- Determine the percentage from the normal distribution.
- The result will be rounded to two decimal places.

(b) **Number of Scores Greater Than 21:**
- Calculate the number based on the normal distribution and the provided number of scores.
- The result will be rounded to the nearest whole number as needed.

**Graph/Diagram Explanation:**

The graph illustrates a normal distribution for standardized test composite scores. It shows:

- A bell curve, which represents the distribution of scores.
- The mean (average) score, denoted as $ \mu $, is 19.6.
- The standard deviation, denoted as $ \sigma $, is 5.2.
- Two specific scores, 19 and 21, are marked along the x-axis.

The graph visualizes the relationship between the scores and their distribution around the mean.

**Form Fields:**

(a) The percent of scores that are less than 19 is ___%.

(Round to two decimal places as needed.)

(b) About ___ scores would be expected to be greater than 21.

(Round to the nearest whole number as needed.)

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