**Problem Statement:**Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 64 miles per hour. The highway patrol's policy is to issue tickets for cars with speeds exceeding 80 miles per hour. The records show that exactly 2% of the speeds exceed this limit. Find the standard deviation of the speeds of cars travelling on California freeways. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.**Solution Process:**Step 1: Understanding the Problem- Given: - Mean (μ) = 64 miles per hour - Speed limit for tickets = 80 miles per hour - Percentage of cars exceeding the speed limit = 2%Step 2: Utilize the Properties of the Normal DistributionStep 3: Z-Score Calculation- Convert the speed limit (80 miles per hour) to a Z-score using the formula for the percentage in the tail of the distribution (2% corresponds to a Z-score using statistical tables or a Z-score calculator).Step 4: Standard Deviation Calculation- Rearrange the Z-score formula to solve for the standard deviation and plug in the known values.**Graphical Representation:**- The image might contain a typical normal distribution curve indicating the mean at the center (64 miles per hour) and the speed limit (80 miles per hour) on the right tail of the curve. The area under the curve beyond 80 miles per hour would be shaded to represent the 2% probability.**Conclusion:**Calculate the final standard deviation by solving the equations and rounding appropriately.

Answered: Image /qna-images/answer/8b33d748-1a40-4017-b03d-0f932faf5e97.jpg

miles Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 64 The highway patrol's policy is to issue hour miles tickets for cars with speeds exceeding 80 hour The records show that exactly 2% of the speeds exceed this limit. Find the standard deviation of the speeds of cars travelling on California freeways. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

miles Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 64 The highway patrol's policy is to issue hour miles tickets for cars with speeds exceeding 80 hour The records show that exactly 2% of the speeds exceed this limit. Find the standard deviation of the speeds of cars travelling on California freeways. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

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

**Problem Statement:**

Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 64 miles per hour. The highway patrol's policy is to issue tickets for cars with speeds exceeding 80 miles per hour. The records show that exactly 2% of the speeds exceed this limit. Find the standard deviation of the speeds of cars travelling on California freeways. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

**Solution Process:**

Step 1: Understanding the Problem
- Given:
- Mean (μ) = 64 miles per hour
- Speed limit for tickets = 80 miles per hour
- Percentage of cars exceeding the speed limit = 2%

Step 2: Utilize the Properties of the Normal Distribution

Step 3: Z-Score Calculation
- Convert the speed limit (80 miles per hour) to a Z-score using the formula for the percentage in the tail of the distribution (2% corresponds to a Z-score using statistical tables or a Z-score calculator).

Step 4: Standard Deviation Calculation
- Rearrange the Z-score formula to solve for the standard deviation and plug in the known values.

**Graphical Representation:**

- The image might contain a typical normal distribution curve indicating the mean at the center (64 miles per hour) and the speed limit (80 miles per hour) on the right tail of the curve. The area under the curve beyond 80 miles per hour would be shaded to represent the 2% probability.

**Conclusion:**
Calculate the final standard deviation by solving the equations and rounding appropriately.

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