The population of weights for men attending a local health club is normally distributed with a mean of 175-lbs and a standard deviation of 29-lbs. An elevator in the health club is limited to 32 occupants, but it will be overloaded if the total weight is in excess of 5984-lbs. Assume that there are 32 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded? average weight = Ibs

Q: A ski gondola carries to the top of a mountain. Assume that the weights of skiers are normally…

A:

Q: an exam score has a mean of 506 and a standard deviation of 100. What exam score corresponds to a…

A: μ  = 506 , σ = 100  Z~ N(0,1)

Q: A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that…

A: Solution-: Given:  In this problem, which type of quantity does the 4 ounces refer to?

Q: The average starting salary of students who graduated from colleges of Business in 2009 was $48,400.…

A: Determine the statement of the hypothesis. The statement of the hypothesis is generally indicated by…

Q: Books in the library are found to have average length of 350 pages with standard deviation of 100…

A: Given: μ=350σ=100x=80

Q: The combined SAT scores for the students at a local high school are normally distributed with a mean…

A: The combined SAT scores for the students at a local high school are normally distributed with, Mean…

Q: A frontliner commutes daily from his home to work. The average time for a one-way trip is 35…

A: Let , X be the time Let , X→N(μ=35 , σ=5) Since , his work starts ate 9:00 AM and he leaves his…

Q: Assume that the number of pieces per bag has a mean of 264 with a standard deviation of 3. use the…

A: Given :  the number of pieces per bag has a mean of , μ=264  a standard deviation of , σ =3   We…

Q: The heights of 5-year-old children are approximately normally distributed with average height of…

A: Given information: The heights of 5-year-old children are approximately normally distributed.…

Q: assume that the mean weight of 1 year-old girls in the Philippines is normally distributed with a…

A: Let X denotes the weight of 1 year-old girls in the Philippines which follows normal distribution…

Q: The average salary of a male professor at a public four-year institution offering classes at the Dr…

A: Given Information : The average salary of a male professor at a public four-year institution…

Q: In the past, a chemical company produced 880 pounds of a certain type of plastic per day.  Now,…

A: From the provided information, Sample size (n) = 50 Sample mean (x̅) = 871 Sample standard deviation…

Q: The contents of 40 cans of Coke have a mean of 12.15 fl oz and a standard deviation of 0.09 fl oz.…

A: Given, mean, x= 12.15 fl oz  standard deviation, σ = 0.09 fl oz population mean, μ = 12 fl oz X ~…

Q: A radio station claims that the amount of advertising each hour has a mean of 16 minutes and a…

A:

Q: The combined math and verbal scores for students taking a national standardized examination for…

A: GivenMean(μ)=810standard deviation(σ)=280

Q: The mean life of a battery is 55 hours with a standard deviation of 6 hours. The manufacturer…

A:

Q: an exam score has a mean of 506 and a standard deviation of 100. What exam score corresponds to a…

A:

Q: Assume that adults have IQ scores that are normally distributed with a mean of 103 and a standard…

A: It is given that the IQ scores follow normal distribution with mean 103 and standard deviation 15.…

Q: The heights of men aged 20 to 29 are normally distributed with a mean of 69.2 inches and a standard…

A: the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2standard normal distribution is a…

Q: The carapace length of an adult is normally distributed with a mean of 17.55 mm and a standard…

A:

Q: The fuel efficiency of cars currently registered in the Commonwealth of Virginia is normally…

A: X follows a Normal distribution with mean = 24 and S.D = 6 Then z=(x-mean)/SD = (x-24)/6  follows…

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

A: Solution: Let X be the cost. From the given information, X follows normal distribution with mean…

Q: . The average number of calories in a bar is 250 and has a standard deviation of 15. The number of…

A: As per our guidelines we are supposed to answer only one question per post so I am solving first…

Q: The luggage weight for individual air travelers on some specific route have a mean of 80 pounds and…

A: Given information: The luggage weight for individual air travelers on a specific route, measured in…

Q: The combined SAT scores for the students at a local high school are normally distributed with a mean…

A:

Q: The distribution of average hours of sleep per weeknight among college students is found to be…

A: Given Mean=6.5 Standard deviations=1.2

Q: A cement manufacturer claims that the average weight of his product is 40 kgs. with a standard…

A: Given: n= 45.0, x̄= 38.71 ,s= 2.35 µ= 40.0, significance level(∝)= 0.01 define hypothesis;- Null…

Q: The lengths of metal bolts are normally distributed with mean μ cm and standard deviation 7 cm. If…

A: Let X be the random variable from normal distribution with mean μ and standard deviation (σ) = 2.5…

Q: The average hours of sleep on a weeknight was 6.9 hours with a standard deviation of 1.5 hours. What…

A: Let, X= The number of hours of sleep on a weeknight. μ=6.9, standard deviation=σ=1.5 We want to…

Q: The time it needs a communications worker to arrange a domestic phone call is normally distributed…

A: It is given that the mean is 50 seconds and standard deviation is 8 seconds.

Q: For a medical study, a researcher wishes to select people in thr middle 75% of the population based…

A: Introduction: Definition: Z-score A Z-score is a numerical measurement that describes a value's…

Q: The weight of potato chips in a large-size bag is stated to be 24 ounces. The amount that the…

A:

Q: The weights of 40 watermelons coming out of a farm are normally distributed with a mean of 6 Kg and…

A: From the given information, Sample size (n) = 40 Ex=6,σx⏞ =1.945 Thus,

Q: Assume that human body temperatures are normally distributed with a mean of 98.23 degrees Upper F…

A: Step-by-step procedure to obtain the percentage using MINITAB:Choose Graph > Probability…

Q: Assume that human body temperatures are normally distributed with a mean of 98.23 degrees Upper F…

A: It is given that human body temperatures follows normal distribution with mean of 98.23 and standard…

Q: The average raintall, recorded to the nearest hundredth of a centimeter, in New York City, for the…

A: (1) Let X be the random variable from normal distribution with mean (μ) = 9.22 and standard…

Q: The combined SAT scores for the students at a local high school are normally distributed with a mean…

A:

Q: me that the heights of women are normally distributed with a mean of 62.9 inches and a standard…

A: To calculate the 75th percentile of a normal distribution, we used the formula as: X=μ+Zσ Where 'X'…

Q: The speed of cars  on a specific road is normally distributed with a mean of 54 mph and a standard…

A: Let us denote X= The speed of cars  on a specific roadGiven that X follows a normal distribution…

Q: In the past, a chemical company produced 880 pounds of a certain type of plastic per day.  Now,…

A: Null Hypothesis: H0: The mean daily yield for the new process is not less than 880. Alternative…

Q: The daily income of bank auditors in SSS Commercial Bank is normally distributed with a mean of P675…

A: Solution: Let x be the daily income of bank auditors in SSS Commercial Bank is normally distributed…

Q: The heights of 82 roller coasters have a mean of 280.7 feet and a population standard deviation of…

A: Given data normally distributed with mean of 280.7 feet, population standard deviation 59.3 feet and…

Q: The average number of days construction workers miss per year is 11 with a standard deviation of…

A: The average number of days construction workers miss per year is 11 with a standard deviation of…

Q: The combined SAT scores for the students at a local high school are normally distributed with a mean…

A: The combined SAT scores for the students at a local high school are normally distributed with a mean…

Q: The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is…

A: Let µ be the mean amount of summer rainfall for the northeastern US.Claim is that the mean amount of…

Q: The annual per capita consumption of bottled water was 33.3 gallons. Assume that the per capita…

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

Q: Butt-to-knee length is approximately normally distributed with a mean of 23.1 inches and a standard…

A: Let X be the butt-to-knee length. Here, X~ N(23.1, 1.22). Then, Z=X-23.11.2~N(0,1)

Q: The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket.…

A: It is given that cost of domestic affairs follows normal distribution with mean $385 and standard…

Q: A cement manufacturer claims that the average weight of his product is 40 kgs. A sample of  45 bags…

A: We have given that  n=45 , Xbar=38.71 , S=2.35 , mu=40

Q: The speeds of motorists passing a particular point on a motorway are found to be normally…

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!