If an hourglass takes an average of 1 hour to empty a full cycle, what probability of time does it take longer than 72 minutes if the standard deviation is 5 minutes? (Make sure to use a percentage!

Q: The average number of electronic messages received in a day on a smartphone is 15. If the standard…

A: Given information: μ=15σ=4

Q: The amount of time it takes students to complete a biology exam is normally distributed with a…

A: Given that, The random variable X is the amount of time takes students to complete a biology exam It…

Q: UPPOSE THE LIFETIMES OF TV TUBES ARE NORMALLY DISTRIBUTED WITH A STANDARD DEVIATION OF 1.1 YEARS.…

A: GIVEN DATA : lifetimes of TV tubes are normally distributed with a standard deviation of 1.1 years…

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5…

A: According to the given information, we have Mean = 5 minutes Standard deviation = 1 minutes

Q: Find P(A), given that P(A) 0.493.

A: Given,      P A=0.493

Q: The amount of time spouses shop for anniversary cards can be modeled by an exponential distribution…

A: Let X is the amount of time ( in minutes ) that a randomly selected spouse spends shopping for an…

Q: The length of human pregnancies from conception to birth varies according to a distribution that is…

A: Given that.   X~N( μ , ?)   μ=266     , ?=16   Z-score =( x - μ )/?

Q: After a researcher adds 6 points to every score in a sample, the standard deviation is found to be s…

A: The question is about change of origin.Introduction :Change of origin :If a no. is added /…

Q: The mean amount of time it takes a kidney stone to pass is 15 days and the standard deviation is 4…

A: GivenMean(μ)=15standard deviation(σ)=4

Q: A particular fruit's weights are normally distributed, with a mean of 522 grams and a standard…

A: GivenMean(μ)=522standard deviation(σ)=32sample size(n)=20

Q: Females have pulse rates that are normally distributed with a mean of 74 beats per minute and a…

A:

Q: The lifespan of a certain insect is believed to follow a normal distribution

A: Life span = X and follows normal with μ=98 and σ=7   We know that (x-μ)/σ follows N(0,1) so,…

Q: A normal distribution (X) has a mean of 100 and a standard deviation of 10. What is the probability…

A: A normal distribution (X) has a mean of 100 and a standard deviation of 10.

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6…

A: Mean=M=6, Standard deviation=S=3X~N(M=6, S=3)

Q: The life of light bulbs is distributed normally. The variance of the lifetime is 225and the mean…

A: The probability of a bulb lasting for at most 540 hours is calculated below:

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 7…

A:

Q: You work at the Quality Department of a photocopier manufacturer. After each over- haul, the time…

A: Introduction: Denote X as the amount of time in years between two consecutive overhauls. It is given…

Q: A population has a mean of 75 and a standard deviation of 15 you randomly sample nine people from…

A: Given population have mean 75 and standard deviation 15. A sample of 9 people from the population is…

Q: The life of light bulbs is distributed normally. The variance of the lifetime is 225225 and the mean…

A: Given that variance = 225, mean = 590 Find the probability of a bulb lasting for at most 607?

Q: If X is exponentially distributed with a mean of 3, can you find a uniform distribution U[a,b] with…

A: The provided information is as follows:The  is exponentially distributed with the mean 3..The mean…

Q: A student will spend 15 hours average each week in class. If the standard deviation is 2 hours, what…

A: Given that mean=15 and standard deviation = 2 Let, X= number of hours spent by a student in the…

Q: The amount of time spouses shop for anniversary cards can be modeled by an exponential distribution…

A:

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5…

A: Here, mean is 5 and standard deviation is 3. We will use z-standard normal distribution.

Q: . The level of blood glucose and diabetes in adults are related. Let X be a random variable measured…

A:

Q: The weight of all 5 pound bags of flour is Normally distributed with mean 5 pounds and standard…

A: Solution: Let X be the weight of all 5 pound bags of flour. From the given information, X follows…

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!