The average time taken to run 10km, X, follows a normal distribution with μμ = 60 minutes and σσ = 15 minutes.   What is the approximate probability that a randomly chosen runner will take more than 45 minutes to complete a 10km ru

Q: Let the data be x1, xn. Suppose that each data-point xi is normally distributed, with unl mean 0 and…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard…

A: Given mean, μ =65 standard deviation, σ=15 X ~ N(μ, σ)

Q: The average height X and weight Y of males in population have a bivariate normal distribution with…

A:

Q: The random variable X has a normal distribution with a variance of 400. If the 33 ^ (rd) percentile…

A: Given, The random variable X has a normal distribution with a variance of 400. If the 33 ^ (rd)…

Q: The compressive strength of concrete is normally distributed with mean 2500 psi and standard 50 psi.…

A:

Q: The annual rainfall in a certain region is modeled using the normal distribution shown below. The…

A:

Q: A sample of university students has an average GPA of 2.78 with a standard deviation of 0.45.  If…

A: Given, A sample of university students has an average GPA of 2.78 with a standard deviation of 0.45.…

Q: What proportion of a normal distribution is located between z = 0 and z = +1.50?

A: Given that.   X~N( 0 , 1 )   μ=0  , ?=1 (for standard normal distribution)    Z-score =( x - μ )/?

Q: A random variable, X, has a normal distribution with mean equal to 1000 and standard deviation equal…

A: Given Information: Mean μ=1000 Standard deviation σ=100 Area to the left of X is 65.17% i.e., 0.6517…

Q: A manufacturer makes screws with a mean diameter of 0.15 cm (centimeters) and a range of 0.10 cm to…

A: Here Given  the screw diameter s range is 0.1 to 0.2 cm .

Q: Find the area in the right tail more extreme than  z⁢= 2.27 in a standard normal distribution.

A: P(Z > 2.27) = 1- P(Z < 2.27) = 1 – 0.988396 =  0.011604 P(Z < 2.27)  = 0.988396 (From Excel…

Q: The compressive strength of samples of cement is normally distributed with a mean and standard…

A:

Q: The lifetime X (in hundreds of hours) of a certain type of battery has a Weibull Distribution with…

A:

Q: The operator of a pumping station has observed that demand for water during early evening ours has…

A: The demand for water during early evening hours is exponentially distributed with mean 100 cfs

Q: A Gaussian random voltage X with zero mean and standard deviation of 4.5 volts appears across 100…

A: Here, X is normally distributed with mean(μ) of 0 volts and standard deviation(σ) of 4.5 volts.

Q: A company sells sunscreen in 400 milliliter (ml) tubes. In fact, the amount of lotion in a tube…

A: From the provided information, Mean (µ) = 396 ml Standard deviation (σ) = 7ml Sample size (n) = 6…

Q: Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard…

A: Solution: From the given information, X follows normal distribution with mean µ=65 and a standard…

Q: Draw the normal curve. Given a normal distribution with population mean is 21 and population…

A: Solution-: Given: μ=21,σ2=64 ∴σ=8 We find x such that, P[X>x]=0.51

Q: Suppose X has a continuous uniform distribution over the interval -1,1. Determine the variance.…

A: We have given that,  X be the continuous random variable from uniform distribution with a = -1 and b…

Q: Suppose X, and X, have a bivariate normal distribution. Then, the condition distribution of X, given…

A: Given: X1 and X2 follow bivariate normal distribution.

Q: The annual rainfall in a certain region is modeled using the normal distribution shown below. The…

A: X be the annual rainfall in a certain region.X~N(μ,σ)where  mean(μ)=30.8 cm  and standard…

Q: For bone density scores that are normally distributed with a mean of 0 and a standard deviation of…

A: The mean is 0 and the standard deviation is 1.

Q: Find the probability of failure free performance of roller bearings over a period of 104 h, if the…

A: Given α=10^7β=1.5

Q: The annual rainfall in a certain region is modeled using the normal distribution shown below. The…

A:

Q: Assume that scores on a bone density test are normally distributed with a mean of 0 and a deviation…

A: It follows normal distribution with mean 0 and standard deviation 1for a randomly selected subject,…

Q: Let X follow normal distribution with mean 50 and standard deviation 4. Let Y follow uniform…

A: Let's see first theoretically, X~N(50,4)Y~N(20,35) Then the value of…

Q: A sociologist wishes to see whether for a certain group of professional women, the average age at…

A: Given,   Sample size = 25 Sample mean = 29.7 Population standard deviation = 1.1   Under the claim,…

Q: The amount of time you have to wait at a particular stoplight is uniformly distributed between zero…

A: A random variable X~U(a=0 , b=5)f(x)=15   ; 0≤X≤5

Q: You are required to generate a random variate from an exponential distribution with rate parameter,…

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Q: Let Xi and X2 be independent random variables each having the standard normal distribution. Consider…

A: Given that x1 and x2 random  variable

Q: The heights of grade 11 students are normally distributed with an average height of grade 11…

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Q: Suppose X has a standard normal distribution. Find the distribution of Y= X2/2

A: Solution-: Suppose X has a standard normal distribution. Find the distribution of Y=X22

Q: The length of time a part lasts after continuous usage follows a Weibull distribution (in hours)…

A: Assume, X be the random variable representing the length of time a part lasts (in hours), which…

Q: For bone density scores that are normally distributed with a mean of 0 and a standard deviation of​…

A:

Q: The ages of expectant parents at Huntsville Women's and Children's Hospital can be approximated by a…

A: Given information: The ages of expectant parents can be approximated by a bivariate normal…

Q: Let xyz be the random quantities of three standard normal distributions, corr(X,Y) = 0.3, corr(X,Z)…

A: Given information: It is given that X, Y, Z are random quantities of three standard normal…

Q: Let x be a continuous random variable that is normally distributed with a mean of 58 and a standard…

A: Given that, Mean = 58 Standard deviation = 17

Q: The time (in minutes) it takes Greg to complete a homework problem is uniformly distributed…

A: X=Time it takes to complete a homework problem X~Ua,bwhere, a=15 and b=28hence, X~U15,28

Q: certain city, the daily consumption of water (in millions of liters) follows approximately a gamma…

A: Here use standard gamma distribution for find function with given parameters

Q: Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard…

A: Assume,  x be the normally distributed random variable. μ be the mean value of x. σ be the standard…

Q: Assume a distribution with mean of 50 and a standard devivation of 12.  For an x-value of 65, the…

A: Given information- Population mean, µ = 50 Population standard deviation, σ = 12

Q: The annual rainfall in a certain region is modeled using the normal distribution shown below. The…

A: Empirical rule: The probability of the observation lies within 1 standard deviation of the mean,…

Q: The average height X and weight Y of males in population have a bivariate normal distribution with…

A:

Q: Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard…

A:

Q: The elongation of a steel bar under a particular load has been established to be normally…

A: The formulae for z-score is given by                                     z = X-μσ where μ is the…

Q: The length of time patients must wait to see a doctor at an emergency room in a large hospital is…

A: Given, The length of time patients must wait to see a doctor at an emergency room in a large…

Q: Describe the chi-squared distribution with parameter v. 3.

A: To Describe: Chi square distribution with parameter v.

Q: Suppose a female patient had 10 blood test over the past year , and the sample mean HC was…

A: Given : population mean , u = 14

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.