A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 207 cm and a standard deviation of 1.5 cm. Find the probability that the length of a randomly selected steel rod is between 204.9 cm and 210.2 cm. P(204.9 cm < X< 210.2 cm) = P(

Q: Find the probability that a randomly selected high school student who took the reading portion of…

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Q: The length of time it takes to find a parking space at 8am follows a normal distribution with a mean…

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Q: The diameter of a brand of tennis balls is approximately normally distributed with a mean of 2.45…

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Q: Moore Reno, an officer in the highway patrol group, observed that the speeds of vehicles on a…

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Q: e monthly utility bills in a city are normally​ distributed, with a mean of ​$100   and a standard…

A: Given: Mean, μ=100 Standard deviation, σ=15 (a)  Probability that a randomly selected utility bill…

Q: The heights of water spinaches, Ipomoea aquatica in Malaysia without fertilizer application are…

A: PX&gt;35=1-Pz&lt;35-205=1-Pz&lt;3=1-0.9987=0.0013

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A: Given data: The population of weights for men (X) is normally distributed with mean and standard…

Q: The mean weight of frozen yoghurt cups in an ice cream parlor is 8 oz. Suppose the weight of each…

A: Let "X" be the weight of frozen yoghurt cups in an ice cream parlor in oz.

Q: A study shows that the cost of new textbook is approximately normally distributed with a mean P142…

A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to…

Q: A student finds that the average price of a movie ticket in Washington is $12.25 and that the…

A: From the provided information, Mean (µ) = $12.25 Standard deviation (σ) = $2 Let X be a random…

Q: The incoming freshman class at North Carolina State University had a mean unweighted GPA of 3.81…

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Q: The incoming freshman class at North Carolina State University had a mean unweighted GPA of 3.81…

A: Given: Sample size (n) = 100 Population mean GPA score μ=3.81 Population standard deviation σ=0.36

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Q: The mean daily production of a herd of cows is assumed to be normally distributed with a an of 37…

A: 37 Obtain the standard z-score for the random variable equals 26.1 liters. The standard z-score for…

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Q: the breaking of a particular rope is normally distributed, with the mean of 350 lbs. and a standard…

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Q: The amount of revenue of a shop is approximately normally distributed with a mean of $4500 and a…

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Q: The average repair cost of a microwave oven is 55$, with a standard deviation of 8$. The costs are…

A: Here, mean is µ = 55, standard deviation is σ = 8, and n = 4.

Q: ounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of…

A: (a) Given: μ=25, σ=7 The corresponding z-value needed to be computed:  The probability that a…

Q: The amount of time between taking a pain reliever and getting relief is nomally distributed with a…

A: Let "X" be the time between taking the medication and getting relief.

Q: The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000…

A: From the provided information, Mean (µ) = 4000 gallons Standard deviation (σ) = 125 gallons X~N…

Q: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of…

A: Given, Mean = 208.9 Standard deviation = 1.4 Sample size = 18   The objective to is find the…

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Q: The average credit card debt for public school teacher is 14,975. If the debt is normally…

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Q: The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard…

A: Given Data Population Mean,μ = 100.0 Population Standard Deviation,σ = 12.0

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Q: The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of…

A: Let X be the length of the aluminum coated sheets. X ~ N(μ, σ) Given,  Mean, μ = 30.05 inches…

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Q: Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard…

A: Solution-: Let, X= The heights of women  Given: \mu=63.6 inches, \sigma=2.5 inches ,n=100 We find,…

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Q: The amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a…

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Q: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of…

A: We have to find P(M &gt; 187.1-cm).

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Q: The heights of 9-year-old children are normally distributed, with a mean of 123 cm and a standard…

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Q: The weight of high school football players is normally distributed with a mean of 195 pounds and a…

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A: Given, μ=34 minutesσ=7 minutesn=9

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Q: The diameter of a brand of tennis balls is approximately normally distributed with a mean of 2.5…

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A: Given information Mean µ = $800 Standard deviation σ = $40

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!