A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 206.8 cm and a standard deviation of 0.5 cm. Find the probability that the length of a randomly selected steel rod is greater than 208.4 cm. P(x > 208.4 cm) = P(z > !! Shade: Left of a value Click and drag the arrows to adjust the values. -4 -3 2 -1.5

Q: q2-- find the mean for the given data. x: 1,1,1,1,1,2,2,2,2,3,3,3,4,5,5,5,6,6,6,6,7,7,7,7,7

A: We know that  Mean  = sum of all observations/total number of observations

Q: Find the probability that the sample mean is between 40 and 50. Sample size is 36 are drawn randomly…

A: From the provided information, Mean (µ) = 45 Standard deviation (σ) = 20 X~N (45, 20) Sample size…

Q: A distribution of values is normal with a mean of 79.5 and a standard deviation of 7.4. Find the…

A: A distribution of values is normal Mean = 79.5 Standard deviation = 7.4

Q: The average hourly wage for manufacturing workers in the United States is $16.08 per hour, with a…

A: Let  be the hourly wage for manufacturing workers in the United States.The average: The standard…

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

A: We have to find probability..

Q: Working in the garden pulling weeds/planting flowers burns an average of 200 calories per hour. If…

A: It is given that  Mean, μ = 200 Standard deviation, σ = 9 Z-Score, Z = ( X - μ )/σ

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

A: Let X be a random variable such that X: the readings at freezing on a batch of thermometers X~N0,1

Q: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of…

A:

Q: Let X = { 1,2,6,9,11}. Find the mean and standard deviation given that X is a sample. %3!

A: The mean for the sample is calculated as follows:

Q: A set of data items is normally distributed with a mean of 200 and a standard deviation of 50. Find…

A:

Q: the average grade is 84 with a standard deviation of 4. What is each grade for -1 2 0 1.5 -1.25

A: Given Mean μ=84Standard deviation σ=4 The formula for Z score isZ=X-μσX=Z×σ+μ

Q: Assume that the readings on thermometers are normally distributed with a mean of 0 degrees Celsius…

A: We have given that Mu= 0 , sigma =1 X~ N ( 0, 1) Zscore=(x-mu)/sigma

Q: find the area of the shaded region. the graph to the right depicts IQ scores of adults and those…

A:

Q: Find f0.01f0.01 for FF distribution with (55,77) degrees of freedom. f0.01

A: The given degrees of freedom is (55, 77).

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

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

Q: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of…

A: mean=145.2cm S.D=2.2cm

Q: Scores on the SAT form a normal distribution with a mean of µ = 500 and standard deviation of σ =…

A: Given Mean(μ)=500standard deviation(σ)=100

Q: Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores…

A: Let x be the IQ score which follows normal distribution with mean 100 and standard deviation 15. The…

Q: 6. The probability that a chocolate biscuit is double wrapped is 0.01, and a box contains 150…

A: Discrete Random Variable: A discreate random variable is a variable whose values can be obtained by…

Q: Let X = number of miles a family travels for summer vacation. X follows a normal distribution with a…

A: From the given information,X follows a normal distribution with a mean of 311 miles and standard…

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

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

Q: Suppose 26% of all small businesses are owned by a particular group of people. In a random sample of…

A:

Q: A final exam in Reindeer Research Studies has a mean of 60 and a standard deviation of 5. If 25…

A: It is given that the mean is 60, the standard deviation is 5 and the sample size is 25.

Q: The amount of rain falling in Waimea Canyon State Park, Kauai is normally distributed with a mean of…

A:

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

A: Given that  Z follows standard normal distribution with mean zero and standard deviation one  Z ~…

Q: 6. Find the variance if X~N(0, ¿) and 95% of the data are between -7 and 7.

A:

Q:

A: Given that IQ scores of adults is normally distributed with mean 100 and standard deviation 15. The…

Q: the mean is 146, and standard deviation is 35. A score of 181 is how many z-scores above the mean?

A:

Q: Help please: Alice throws darts at a circular target of radius r and is equally likely to hit any…

A: Here given that Alice throws darts at a circular target of radius r and is equally likely to hit any…

Q: The proportion of a in the tail of a gold distribution can be never be more than .50 true or false

A: We have to find given statement is true or false

Q: Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean…

A: Since the probability for the given variable (that is discrete in nature), i.e., the probability of…

Q: Find the are of the shaded region. The graph depicts the iq scores of adults and those 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!