In this section, we mentioned that the total area under any curve representing the distribution of a variable equals 1. Explain why.

Q: According to the Distribution of Z table, ______ % of area is below a Z value of -0.50?

A: Using a standard normal table area to the left of z score, look up for z value -0.50 i.e., -0.5 in…

Q: Can you help me complete the figure below using the Empirical Rule to show the values at the…

A: The empirical rule of Normal distribution predicts that 68% of observations falls within the first…

Q: A new type of vehicle tires is released on the market with a rate of tire cracking: on average one…

A: Given information: Average number of cracks every 2000 km = 1  Average number of cracks every 500 km…

Q: For the Central Limit Theorem, the idea is that the more values within your data set, the more the…

A: We are given below Histogram.

Q: A measure computed from the entire population is a will not change. As long as the population does…

A: Here , our aim is to find the blanks. Since , the parameter is a number which describe the entire…

Q: A group of students practiced a series of trials at a shooting range. Their scores are plotted in…

A: The difference score of the group is obtained below: Difference=Group 2-Group 1=4-2=2

Q: Calculate on the maximum percentage error in the volume of the cylinder-shaped oil barrel if the…

A:

Q: Explain how the available noise power in an electronic circuit can be estimated.

A: Answer: For the given data,

Q: If each of the dimensions of a rectangular box is measured with an error not exceeding 1%, what i…

A:

Q: Is the ratio of the number of times an event actually occurs to the total number of trials or times…

A: The Theoretical Probability is the probability calculated based on reasoning and Experimental…

Q: Find the quantity (in thousands) that minimizes Shaki's average cost for making danglies.

A: The minimum or maximum of a quantity is obtained by taking the first derivative of the equation and…

Q: Briefly explain the concept of cross power density spectrum.

A: A spectral analysis that compares two signals is known as cross power spectral density (CPSD) or…

Q: How can you sometimes estimate quantities like distance traveled, area, and average value with…

A: Let the function defined over [a,b]. And the interval is divided into n subintervals of equal width

Q: Use Simpson's Rule to determine the average temperature in a museum over a 3-hour period

A: In this question, we use the Simpson rule to approximate the average value of temperature for 3…

Q: Complete the table above by including: Measurement Type (i.e., nominal, ordinal, continuous) for all…

A: Solution

Q: What positive number added to its reciprocal gives the minimum sum?

A:

Q: The general aviation Manufacturers Association has reported the average annual number of hours flown…

A: Mean = 120 Standard deviation = 30

Q: To approximate the area under the curve in Figure 1, we can use rectangles as illustrated in Figures…

A: Here is the solution of the given problem. Right Hand Riemann Sum

Q: Determine an upper bound for the total amount of Coke that could have flowed into the room during…

A: Given data of coke factory. At time t=0, R(0) = 1.2 gallons/minute At time t=12 ,R(12) = 1.4…

Q: The radius of a cell is measured to be 6 microns with an error of plus or minus 0.4 microns. What is…

A: Given that: Radius of cell=6 microns.Error in radius=±0.4 microns

Q: What is the average speed in the attached image?

A: From the given graph  Base1= 200 Base 2 = 100.  Height = 40  Area of trapezium = 1/2 (base1+base2)…

Q: hy is an interval estimate for the population preferred to a point estimate?

A: We know that  Point estimate : It is a single value (Statistic) used to estimate the population…

Q: What is the image of (−7,5) after a dilation by a scale factor of 22 centered at the origin?

A: This question is about dilation of point

Q: The rectangles of a histogram is proportional to O Cumulative frequencies of the distribution O…

A: Here we have identify the rectangle of histogram proportional to

Q: Construct your own problem involving related rates.

A:

Q: What is the image of (3,-12) after a dilation by a scale factor of centered at the origin?

A: TO find the image of the point, multiply the given point by the scale factor.

Q: Use Simpson's rule to estimate the total anm discharge in the first 24 hours. TO

A: Simpsons rule for the function f(x) over [a,b] is given as:…

Q: A cube of side 2 cm is to be made. However, due to erroneous measurement, the actual side of the…

A:

Q: A vertical line drawn through a normal distribution at z = -1.30 will separate the distribution into…

A:

Q: Describe the key characteristics of hyper exponential distribution?

A: The hypeexponential distribution is an example of phase-type distribution where n phases are in…

Q: Suppose a biologist collected data on the weight of 50 lab rats that were 4 weeks old. The boxplot…

A: First of all, we know that A boxplot gives us 5 things: Minimum value.1st quartile, Median, 3rd…

Q: Any quantity that is computed from a sample is called

A: Sample :  It is subset of population

Q: According to the Distribution of Z table, ______________ % of area is below a Z value of -1.16?

A: Z value = -1.16 Percentage of area that is below a Z value of -1.16 is given as,

Q: One value is circled in each distribution. Is there a difference between what is represented by the…

A: Since Figure A and B represents two Histograms. The highest peak represents the nearest value to…

Q: variable X, representing the average time to failure for an automobile battery,can be written as:…

A: Here, the distribution of the variable X, represent the average time to failure for an automobile…

Q: The edge x of a cube is measured with an error of at most 0.5%.What is the maximum corresponding…

A: Given: Let x be the edge of the cube with an error of 0.5%.

Q: Explain, whether the data can be calculated if the hypergeometric distribution is not known the…

A: Please find the explanation below. Thank you

Q: What is the image of (4,-8) after a dilation by a scale factor of centered at the origin?

A: Given that point is (4,-8)  After the dilation by a scalar factor of (1/4) center at the origin .

Q: Suppose that the time spent by children in front of the television set per year has the distribution…

A: We have given that X ~ N (µ, σ )= N(1500 , 250) Mean(µ) = 1500Standard deviations (σ) = 250

Q: For reasons of safety, a study of bears involved the collection of various measurements that were…

A: Enter the Given data in Excel as shown below

Q: An object moves along a line, where its velocity function is as described by the graph below. What…

A: Given function is., Distance of the function on the interval [2, 8] Distance is nothing but the…

Q: A study at Harvard found that 44% of their students binge drink.  You are at Princeton doing a…

A: According to the provided information, a study at Harvard found that 44% of their students binge…

Q: a random sample of 25 children is selected and each is given several pieces of yummy gummy candy.…

A: Given, total number of children n= 25 No of children like candy x = 22

Q: A study wants to look at what % of the population is tall. If they want to estimate the percentage…

A:

Q: The normal price on a compressor is $280 but it is discounted by 20%. What is the discounted price?

A:

Q: The toco toucan, the largest member of the toucan family, possesses the largest beak relative to…

A: The regression analysis is conducted using EXCEL. The software procedure is given below: Enter the…

Q: Give two reasons why the use of smooth curves to describe shapes of distributions is helpful.

A: Reasons for using the smooth curves on priority:In order to identify, the shape of the distribution…

Q: The radius r of a circle is measured with an error of at most 2%.What is the maximum corresponding…

A: To determine:                             The maximum corresponding percentage error in computing…

Q: What is the area of the light green shaded region labeled as section 1? (round your answer to 3…

A: The given diagram is

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!