The mean is µ = 15.2 and the standard deviation is Η = 0.9. Find the probability that X is between 14.3 and 16.1.

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…

A:

Q: For a continuous variable with normal distribution where the mean is 22.5 and the standard deviation…

A: (1) Obtain the probability that X is less than 23. The probability that X is less than 23 is…

Q: Assume that females have pulse rates that are normally distributed with a mean of μ=74.0 beats per…

A: Given, Assume that females have pulse rates that are normally distributed with a mean of μ=74.0…

Q: Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean…

A: Answer:- Given, The readings at freezing on a batch of thermometers are normally distributed with a…

Q: The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/45…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Assume that a certain bacteria contaminated in a gallon of milk is normally distributed with a mean…

A: Given,mean(μ)=2500standard deviation(σ)=46.3

Q: Assume that adults have IQ scores that are normally distributed with μ=38 and a standard deviation…

A:

Q: Find the X value corresponding to z = +0.75 for a distribution with population mean of 90 and…

A: Solution: From given information, µ=90, σ=12 and z=0.75.

Q: Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood).…

A: The sample size is 36The sample mean is 8.8The sample standard deviation is 3.5We have to test…

Q: X is a normally distributed random variable with a standard deviation of 3.50. Find the mean of X…

A:

Q: Assume that females have pulse rates that are normally distributed with a mean of μ=76.0 beats per…

A: Given data, μ=76.0  σ=12.5  P(X<83)=?

Q: Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean…

A: The Z-score of a random variable X is defined as follows: Z=(X–µ)σ Here, µ and σ are the mean and…

Q: Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood).…

A:

Q: ez-score for x = 61 is . So 61 is standard deviations (Choose one) ▼ the mean μ = 56. X

A: It is given thatMean, μ = 56Standard deviation, σ = 20Z-Score, Z = ( X - μ )/σwhere, Z be the…

Q: Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean…

A: Answer:- Given, The readings at freezing on a batch of thermometers are normally distributed with a…

Q: Corey scores X = 70 on his first exam, for which the entire class scored a mean of µ = 78 and…

A: From the given information, let X be the Corey’s score on his first exam. X = 70. Mean score of the…

Q: Ages of Gamblers The mean age of a sample of 25 people who were playing the slot machines is 49.9…

A: The Welch's t - test should be used to compare the mean differences between two population groups…

Q: random variable is normally distributed. It has a mean of 241 and a standard deviation of 17. For a…

A: Given that.   X~N( μ , ?)   μ=241 , ?=17   Z-score =( x - μ )/?

Q: A random variable is normally distributed. It has a mean of 241 and a standard deviation of 17.…

A: given data normal distributionμ = 241σ = 17n= 10

Q: A normal distribution has mean μ = 60 and standard deviation σ = 20. Find and interpret the z-score…

A: Step 1: State the given data: raw score, x = 75population mean, µ = 60population standard deviation,…

Q: A random variable is normally distributed. It has a mean of 241 and a standard deviation of 17. For…

A: given data, normal distributionμ=242σ=17we have to find out the given probabilties.

Q: Find the mean and standard deviation for the binomial distribution when p = 3/8 and n= 235.

A: Given p=3/8, n=235

Q: A random variable is not normally distributed, but it is mound shaped. It has a mean of 18 and a…

A: GivenMean(μ)=18standard deviation(σ)=2sample size(n)=40

Q: If W is a normally distributed with the mean of 225, find the standard deviation, given that P(X <…

A: Given data: Mean  = 225 find: Standard deviation

Q: The mean and variance of a binomial distribution are 3 and 2 respectively. Find P(X < 3). 9.

A: Given data: np=3 np(1-p)=2

Q: Assume that x has a normal distribution with the mean=4 and standard deviation=6. Find the…

A: It is given that, X has a normal distribution with mean, μ =4 and standard deviation, σ =6.

Q: Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard…

A: We have given thatMean(µ) = 0Standard deviations (σ) = 1X ~ N (µ, σ )= N(0, 1)

Q: We take a random sample of 16 scores from a Math Exam and the sample mean is 80 (the population…

A: Sample mean =80.Sample standard deviation, s =15.The sample size, n is 16.

Q: x=200,μ=225,σ=10 x=1,μ=−1,σ=2 x=0,μ=−400,σ=200 x=12,μ=21,σ=3 The x value of ? lies the greatest…

A: Given information are,Let, (a) x=200, μ=225, σ=10(b) x=1, μ=−1, σ=2(c) x=0, μ=−400, σ=200(d) x=12,…

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100and a standard…

A: From the provided information, Mean (µ) = 100 Standard deviation (σ) = 20 Let X be a random variable…

Q: IQ is normally distributed with a mean of 100 and a standard deviation of 15.  When selecting…

A:

Q: A random variable is not normally distributed, but it is mound shaped. It has a mean of 18 and a…

A: given data population mean ( μ ) = 18population sd ( σ ) = 2sample size (n) = 13find mean of the…

Q: The lifetime X of a widget has a Weibull distribution with parameters a = 2 and B = 5. The mean…

A: The mean is 4.43 and standard deviation is 2.316.

Q: robability that the plant will not be inundated for a period of 5 years? [Note the mean rate of…

A: Given: Probability of inundation  = 0.020 Mean rate if flood for inundation per year  = 0.012 Mean…

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard…

A: Given : Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a…

Q: onsider a population that has a score of X = 15 associated with a z-score of +1.50. What does this…

A: Given: X=15  z-score =+1.50

Q: If P(−b<z<b)=0.98P(-b<z<b)=0.98, find b.

A: Given that Z ~ N(0, 1) And P(-b &lt; Z &lt; b) = 0.98

Q: A Lumix Panasonic camera has a rechargeable battery. The battery life before recharging is needed…

A: Given: A Lumix Panasonic camera has a rechargeable battery. Let X be a random variable that…

Q: Suppose that replacement times for washing machines are normally distributed with a mean of μ=8.7…

A: For a variable distributed normally, i.e for X~N(μ, σ) the z-score for X is, Z=X-μσ; Z~N(0,1)…

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!