21 The life of a drill bit has a mean of 16 hours and a standard deviation of 2-6 hours. Assuming a normal distribution, determine the probability of a sample bit lasting for: (a) more than 20 hours (b) fewer than 14 hours

Q: Annual food consumption survey shows that number of instant food meals consumed per month by…

A:

Q: A manufacturer produces a commodity where the length of the commodity has approximately normal…

A: From the provided information, Population mean (µ) = 10.3 inches Population standard deviation (σ) =…

Q: The average life of a electric rice cooker is 5 years, with a standard deviation of 1 year. Assume…

A: Obtain the probability that the mean life of a random sample of 9 machines falls between 5.7 and 8.1…

Q: Scores on an employment test follow a normal distribution with a mean of 98 and a standard deviation…

A: Here, µ=98 and σ=17.

Q: What is the mean of the distribution of sample means? = μx ft What is the standard deviation of the…

A: It is given that Mean = 185.6 And SD = 63.5 Sample size n = 142

Q: In a random sample of 100 trout, the average weight is 10 pounds, with standard deviation (s) = 0.6,…

A: Answer: From the given data, Sample size(n) = 100 mean (x¯) = 10 standard deviation(s) = 0.6

Q: In a random sample of 80 trout, the average weight is 8 pounds, with standard deviation (s) = 0.9,…

A: Answer: From the given data, Sample size(n) = 80 mean = 8 Standard deviation(s) = 0.9

Q: What is the mean of the distribution of sample means? What is the standard deviation of the…

A: Given that, A population is Normal with the parameters: μ=217.4 and σ=33.8 Sample size (n) = 245

Q: Find the z score value for a data value of 15. Z-score = ? (Round to 2 decimal places)

A: It is given that the random variable is normally distributed with  Mean, μ = 12 Standard deviation,…

Q: A population is normally distributed with mean 11.5 and standard deviation 5. Find the probability…

A:

Q: certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 years.…

A: Given data,Mean μ=3sd    σ=0.5Let X denotes battery lifeP(X>3.5)=?

Q: A certain computer spare part has an average life of 400 days with a standard deviation of 10 days.…

A: The mean and standard deviation are 400 and 10 respectively.

Q: The average monthly number of jobs available in Area A is 3, 000. If we assume a normal distribution…

A: We have given that,  X be the random variable from normal distribution with average or mean (μ) =…

Q: The population mean rushing yards gained in the 2005 NFL season by runners with at least one…

A: Mean ()=160standard deviation ()=174sample size(n)=10

Q: If babies have birth weights that are approximately normally distributed with mean 3.3kg and a…

A: Given :  μ=3.3 kgσ=0.55 kgX~N(μ=3.3,σ2=(0.55)2)  We want to find, P(X > 5) = ?

Q: total cholesterl in children ag 10 to 15 with a mean of 91 mg and a standard deviation 22.4 in a…

A: Sample size n =20 Population mean μ =91 Population standard deviation =22.4

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A: Obtain the mean number of students that will come see me on a particular day. The mean number of…

Q: Assume that blood pressure readings are normally distributed with a mean of  125  and a standard…

A: From the provided information, Mean (µ) = 125 Standard deviation (σ) = 4.7 X~N (125, 4.7) Sample…

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A: Given data: Normal distribution is given Mean = 100 Standard deviation  = 15 To find: The…

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A:

Q: The birth weights of males born full-term vary according to an approximately normal distribution…

A: Given,mean(μ)=3.4standard deviation(σ)=0.5

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A: Let us consider that the length commodity which is produced by a manufacturer is denoted by X which…

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

Q: A manufacturer produces a commodity where the length of the commodity has approximately normal…

A:

Q: A manufacturer produces a commodity where the length of the commodity has approximately normal…

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

Q: Number of weekly grocery deliveries requested at Wal-Mart is a normal random variable with mean m =…

A:

Q: A manufacturer produces a commodity where the length of the commodity has approximately normal…

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Q: height in the male population is normally distributed with a mean height of 5–11 (71 in.) and a…

A: Here is given that mean is 71 inches and standard deviation is 4 inches. 6 ft is equal to 72 inches.

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A: Given data,μ=0.4σ=0.02P(X>0.418)=?

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A: [ Note: Since you have posted a question with multiple subparts, we will solve the first three…

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A: Here it is given that the growth of sunflower is normally distributed with mean=3.18 and SD=0.52…

Q: A radar makes a random error in measuring the distance of an aircraft as follows. If the true…

A: Problem can be solved using Standard Error formula and Standard Normal Table.

Q: Scores on an employment test follow a normal distribution with a mean of 222 and a standard…

A:

Q: In a random sample of 87 trout, the average weight is 6 pounds, with standard deviation(s) = 0.8,…

A: Answer: From the given data, Sample size(n) = 87 mean (x¯) = 6 Standard deviation(s) = 0.8

Q: According to a poll, individuals keep their mobile phones for an average of 1.4 years before…

A: Normal Distribution: A continuous random variable X is said to follow Normal distribution with…

Q: Assume the population data in this scenario is normally distributed. a. What is the probability that…

A: Let X be the random variable from Normal distribution with mean (μ) = 120, standard deviation (σ) =…

Q: The monthly In distributed, with mean of $100 standard deviation of $13. Find the probability that a…

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Q: A manufacturer produces a commodity where the length of the commodity has approximately normal…

A: Given:Let X: Length commodity

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!