A study discovered that Americans consumed an average of 12.4 pounds of chocolate per year. Assume that the annual chocolate consumption follows the normal distribution with a standard deviation of 3.2 pounds. Complete parts a through e below. 0.1446 (Round to four decimal places as needed.) b. What is the probability that an American will consume more than 11 pounds of chocolate next year? 0.6691 (Round to four decimal places as needed.) c. What is the probability that an American will consume between 10 and 13 pounds of chocolate next year? 0.3477 (Round to four decimal places as needed.) d. What is the probability that an American will consume exactly 12 pounds of chocolate next year? 0 (Round to four decimal places as needed.)

Q: Find the z-score for the value 62, when the mean is 56 and the standard deviation is 2. O A. z=3.00…

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

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

A:

Q: The average per capita income for residents of Pennsylvania is $32,711 with a standard deviation of…

A:

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

A: Given information Population mean µ = 100 Standard deviation σ = 20 We have to find the probability…

Q: Suppose that the exam scores of a statistics class were normally distributed with a mean of 94 and…

A: Solution: Let X be the exam score of a statistics class. From the given information, X follows…

Q: A population of insect weights is normal with the mean of u = 16. If the probability of a weight…

A: Here the given information is A population of insect weights is normal with the mean of u = 16. If…

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

A: Given information-We have given that adults have IQ scores that are normally distributed.μ= 105σ =…

Q: Determine the probability that a boy who was enrolled at NEU would weigh higher or equal to 112 lbs.…

A: given data  normal distribution μ = 110σ = 5 P(x≥112) = ?

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

A: as per bartleby guideline expert have to answer first three subpart only dear student please upload…

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

A: Given that: Z is standard normal Distributed with i.e. mean µ =0 and standard deviation σ =1 now…

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

A: Let "X" be the IQ score of the adults.

Q: Which among the value approximately equal to P(Z>-1.20) A.) 0.1151 B.) 0.3849 C.) 0.7698 D.) 0.8849

A: Let Z be the random variable from normal distribution the we will find the probability    P(Z>…

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

A: Let "X" be the IQ score of adults.

Q: om's commuting time from his residence in Carmel to the IUPUI campus has a normal distribution.  The…

A: Given that  The residence in Carmel to the IUPUI campus has a normal distribution.  Standard…

Q: ssume that a randomly selected subject is given a bone density test. Bone density test scores are…

A:

Q: A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.67 lb, the…

A: The highest weight is 5.67 lb.Mean of all weights (x̄) = 2.242The standard deviation of weight (s) =…

Q: The average number of days absent per student per year at West Valley School is 17 days with a…

A: mean = μ = 17standard deviation = σ = 4

Q: The average number of strawberries that come in a pint is 27.9, with a standard deviation of 7.8.…

A:

Q: The distribution of head circumference for full term newborn female infants is approximately normal…

A: The distribution of head circumference for full-term newborn female infants is approximately normal…

Q: Systolic blood pressure is a measure of the force your heart exerts on the walls of your arteries…

A: GivenMean(μ)=116.91standard deviation(σ)=6.354and given adult's systolic blood pressure is…

Q: Seattle, Washington, averages m=34 inches of annual precipitation. Assuming that the distribution of…

A: From the provided information, Mean (µ) = 34 inches Standard deviation (σ) = 6.5 inches Let X be a…

Q: The weekly mean income of a group of executives is $1,000 and the standard deviation of this group…

A:

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

A: Given information Population mean µ = 100 Standard deviation σ = 20 We have to find the probability…

Q: As of 2020, 83 pitchers have been inducted into the Major League Baseball Hall of Fame. The…

A: Given that, The number of winning games pitchers played is approximately normal with a mean of 250…

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

A: Calculation: Let X denote the temperature reading of a randomly selected thermometer. The…

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

A: From the provided information, Mean (µ) = 100 Standard deviation (σ) = 15

Q: The middle 50% of the heights are between what two values? Round to one decimal place.

A: Here Given, Assume that women have heights that are normally distributed with a mean of 63.6 inches…

Q: Based upon past flight data, the average weight of checked baggage was 44.5 pounds with a standard…

A: Given that  X~N( μ = 44.5 , ? = 3.6 ) μ = 44.5 , ? = 3.6 , n = 400 Z-score =( x - μ )/?

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

A: Let X denote the IQ scores of adults. Given that X follows N(mean = 105, SD = 20), then Z = (X -…

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

A: Let X is defined as the adult have IQ scores that are normally distributed with mean of 100 and…

Q: The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 118…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The average number of miles driven on a full tank of gas in a certain model car before its​ low-fuel…

A: It is given that the mean is 399 and the standard deviation is 36.

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

A: μ=105 Sd=20 P( 85<x<125)=?

Q: normally distributed data set has

A: Given that a normally distributed data set has a mean of 0 and a standard deviation of 2.

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!