According to a recent reporting on a standardized test, the average ERW (English, Reading, Writing) score for students in a particular state was 521. Assume the scores are Normally distributed with a standard deviation of 96. Answer parts a through c below including an appropriately labeled and shaded Normal curve for each part.

Q: On a standardized test, scores are normally distributed with a mean of 400 and a standard deviation…

A: Given data,μ=400σ=80P(X<x)=80%=0.80x=?

Q: On a statistics exam, the mean score was 80 and there was a standard deviation of 7. If a student's…

A: Given data, μ=80σ=7If x=92z=?

Q: Suppose the heights of women at a college are approximately Normally distributed with a mean of 66…

A: Measures of position:The most common measures of position are percentiles, quartiles and standard…

Q: for a population with a standard deviation of 5 and mean of 40, draw a bell shaped curve, marking…

A: In statistics, the empirical rule says that for normal distribution, 68%, 95%, and 99.7% of the…

Q: On the Gulf Freeway at 7:00 AM, the average travel time from Beltway 8 to Downtown is 29.5 minutes…

A: From the given information,   Mean = 29.5 Standard deviation = 11.2   The objective is to calculate…

Q: The mean annual automobile insurance premium is $950, with a standard deviation of $175. The data…

A:

Q: According to a recent survey, the salaries of assistant professors have a mean of $40,756 and a…

A: We want to find the probability

Q: In a county male height is normally distributed with a mean of 175 cm and a standard deviation of 6…

A:

Q: The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard…

A: It is given that the depth of the snow follows a normal distribution with mean 2.5 inches and…

Q: The mean speed of a sample of vehicles along a stretch of highway is 67 miles per hour, with a…

A: From the provided information, Mean (µ) = 67 miles per hour Standard deviation (σ) = 2 miles per…

Q: The mean SAT verbal score is 417​, with a standard deviation of 99. Use the empirical rule to…

A: It is given that the mean is 417 and the standard deviation is 99.

Q: The wind speeds throughout the month of April were normally distributed with a mean of 17 mph and a…

A: Given: Mean(μ)=17standard deviaion(σ)=4

Q: The mean score for a test is 87 with a standard deviation of 12.  Assuming a normal distribution for…

A: Given,mean(μ)=87standard deviation(σ)=12

Q: Assume that the heights of women are normally distributed with a mean of 64.9 inches and a standard…

A: Given: Heights of women = X X follows Normal distribution with mean 64.9 inches and standard…

Q: A major department store has determined that its customers charge an average of $500 per month, with…

A:

Q: In which distribution shape does the Standard Deviation Rule apply?

A:

Q: the mean weight of a group of boys is 145 lb, with a standard deviation of 4lb. if the weights are…

A:

Q: . The Fresha Tea Company packs tea in bags marked as 250 grams. A large number of packs of tea were…

A: As per our guidelines we are suppose  to answer only one question1)GivenMean(μ)=255 gramsstandard…

Q: A set of data items is normally distributed with a mean of 80 and a standard deviation of 9 .…

A: Given A set of data is normally distributed with mean of 80 and standard deviation of 9 and x=71.so,…

Q: A manufacturer claims that the mean weight of its ice cream cartons is 10 ounces with a standard…

A:

Q: As reported in Runner's World magazine, the times of the finishers in the New York Cit km run are…

A:

Q: The length of time it takes a Grade 11 student to play the Candy Crush computer app follows a normal…

A: Given that  The length of time it takes a grade 11student to play the candy crush computer is…

Q: On a standardized exam, the scores are normally distributed with a mean of 35 and a standard…

A:

Q: The mean speed of a sample of vehicles along a stretch of highway is 64 miles per​ hour, with a…

A: Given, μ=64σ=4P(52<X<76)=?

Q: The results of a recent survey indicate that the average new car costs $23,000, with a standard…

A: It is given that the mean new car cost is $23,000 with a standard deviation of $3,500.

Q: The United States Forest Service is interested in determining the percentage of acreage in Yosemite…

A:

Q: The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152…

A: a) Consider that the mean and standard deviation of a random variable X are µ and σ, respectively.…

Q: The heights of adult men in America are normally distributed, with a mean of 69.4 inches and a…

A: Mean (Adult men) = 69.4 Standard deviation (Adult men) = 2.68 Mean (Adult women) = 64.3 Standard…

Q: In an all boys school, the heights of the student body are normally distributed with a mean of 69…

A:

Q: The heights of American men are normally distributed with a mean of 65.3 inches and a standard…

A:

Q: The mean height of trees in the virgin forest of Zambales is 42 feet and the standard deviation is 3…

A: The mean height of trees in the virgin forest of Zambales is 42 feet and the standard deviation is 3…

Q: The Atlanta Braves baseball team has a mean batting average of 250 with a standard deviation of 20.…

A:

Q: The average grade for an exam is 74, and the standard deviation is 7. If 12% of the class is given…

A: Let the random variable X denote grade score. Then, X~Nμ, σ2 with μ=74 and σ=7. Let α be the lowest…

Q: A popular soft drink is sold in 1-liter (1,000-milliliter) bottles. Because of variation in the…

A: A continuous random variable X is said to follow Normal distribution with parameters μ and σ2 if…

Q: The data set has size 90. Approximately how many observations lie within two standard deviations…

A: The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3…

Q: The data set has size 40. Approximately how many observations lie within two standard deviations to…

A: 68-95-99.7-rule: Let X be an observation from a normal distribution, having mean µ and standard…

Q: A standardized test has a mean of 50 and a standard deviation of 4. Which of the following is the…

A: The normal distribution  in the center are generally denser and basically less denser at tails.…

Q: the mean weight of a group of boys is 145 lb, with a standard deviation of 5lb. if the weights are…

A: We have to find correct answer..

Q: In the province of Iloilo,the set of recorded midday temperature readings for the month of February…

A: Given, 10.5% of recorded temperature readings were under 28°C, and that 33% were above 30°. The…

Q: A given set of data has a specific standard deviation. Describe what will happen to the standard…

A: Answer: The standard deviation of new data is remains same as original data. As a general rule, the…

Q: The heights of male students are normally distributed with a mean of 170 cm and a standard deviation…

A: The heights of male students are normally distributed with a mean of 170 cm and a standard deviation…

Q: On a standardized exam, the scores are normally distributed with a mean of 170 and a standard…

A: We have to find z score..

Q: in a test of a lifelong brand of tires , a survey revealed that the mean life was 35,000 mikes and…

A: Let the random variable X be the life of tires.  The random variable X follows Normal distribution…

Q: Given an approximately normal distribution with a mean of 175 and a standard deviation of 37,…

A: Given info: Here, mean is 175 and standard deviation is 37.

Q: The scores of students on an exam are normally distributed with a mean of 193 and a standard…

A:

Q: The mean score of a competency test is​ 82, with a standard deviation of 2. Between what two values…

A: Given that : Mean (u) = 82 S. D. (sgma ) = 2 Assume data set is nell shapped i.e  standard normal.

Q: The weights for a baby boy is normally distributed with a mean score of 7lbs and a standard…

A: Question is incomplete. Please upload the complete question. I can do these type of questions with…

Q: m and 5.50 m. What is the standard deviation

A: Introduction: The Standard Deviation in descriptive statistics is the degree of dispersion or…

Q: The data set has size 80. Approximately how many observations lie within two standard deviations to…

A: Empirical rule: On a normal distribution about 68% of data will be within one standard deviation of…

Q: A set of data items is normally distributed with a mean of 60 and a standard deviation of 9. Convert…

A:

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!