**Random Number Selection and Distribution Analysis**In this exercise, we investigate the distribution and probabilities concerning a computer that selects a number \( X \) from the interval 4 to 12 randomly and uniformly. All answers should be rounded to four decimal places where required.1. **Distribution of \( X \)** a. **Question:** What is the distribution of \( X \)? **Answer:** \( X \sim U(\_\_\_\_, \_\_\_\_) \) In this part, \( X \) follows a uniform distribution over the range 4 to 12.2. **Distribution of Sample Mean \( \bar{X} \)** b. **Question:** Suppose that the computer randomly picks 37 such numbers. What is the distribution of \( \bar{X} \) for this selection of numbers? **Answer:** \( \bar{X} \sim N(\_\_\_\_, \_\_\_\_) \) Given 37 selections, \( \bar{X} \) will follow a normal distribution due to the Central Limit Theorem. The parameters need to be calculated based on the given range.3. **Probability Calculation** c. **Question:** What is the probability that the average of 37 numbers will be less than 8.9? This involves calculating the probability that \( \bar{X} \) is less than 8.9, based on the normal distribution parameters derived in part b.Each step requires careful consideration of statistical principles, including uniform and normal distributions, as well as the Central Limit Theorem.

It is given that A computer selects a number X from 4 to 12 randomly and uniformly. The pdf of…

Answered: a. What is the distribution of X? XU(…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A computer selects a number X from 1 to 8 randomly and uniformly. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U b. Suppose that the computer randomly picks 38 such numbers. What is the distribution of a for this selection of numbers. T - N( c. What is the probability that the average of 38 numbers will be more than 3.6?
2. Graph each distribution using a probability histogram. a) P(x) b) P(x) 0.05 1 12 4 0.13 5 12 1 6. 0.24 8. 0.38 1 3 10 0.12 1 12 0.05 3 14 0.03
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24. Use the probability distribution to complete parts (a) through (d) below. The probability distribution of number of televisions per household in a small town X 0 3 P(x) 0.03 0.54 (a) Find the probability of randomly selecting a household that has one or two televisions. The probability is (Type an integer or a decimal. Do not round.) (b) Find the probability of randomly selecting a household that has two or more televisions. 1 0.11 2 0.32 The probability is (Type an integer or a decimal. Do not round.) (c) Find the probability of randomly selecting a household that has between one and three televisions, inclusive. The probability is (Type an integer or a decimal. Do not round.) (d) Find the probability of randomly selecting a household that has at most two televisions. The probability is (Type an integer or a decimal. Do not round.)
Answer D
Answer A-C
A computer selects a number X from 4 to 11 randomly and uniformly. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U(| b. Suppose that the computer randomly picks 39 such numbers. What is the distribution of a for this selection of numbers. a - N( c. What is the probability that the average of 39 numbers will be less than 6.6?
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a. What is the distribution of X? XU( b. Suppose that the computer randomly picks 37 such numbers. What is the distribution of a for this selection of numbers. - N( c. What is the probability that the average of 37 numbers will be less than 8.9?