paint manufacturer produces cans of paint of nominal volume 2 litres. In fact the volume of paint in a can is a Normal random variable with mean 2.02 litres and standard deviation 0.02 litres. A single can is examined; the probability that it contains less than 2 litres is (3 d.p.)?
Q: A random sample of size 40 was drawn from a normal distribution with the mean 50 and standard…
A: From the provided information, Mean (µ) = 50 Standard deviation (σ) = 10 X~N (50, 10)
Q: A research study investigated differences between male and female students. Based on the study…
A: Let "M" be the mean GPA of students.
Q: in a certain region, the mean annual salary for electricians is $58,650. Let x be a random variable…
A: GivenMean(μ)=58650standard deviation(s)=1890sample size(n)=40
Q: Ms. Berry is concerned about the average amount of food Fred, the elephant, eats each day. Zookeeper…
A:
Q: Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took…
A:
Q: The size of shrimp influences the number of shrimp in each packaging. By definition, jumbo shrimp…
A:
Q: A. If one male passenger is randomly selected from the airliner, find the probability that he will…
A:
Q: Consider the continuous normal random variable, X = {a typical customer’s expenditure at Baby-Toy…
A: Let the typical customer expenditure at Toy store be X. The mean and standard deviation of the…
Q: uppose the random variable X follows a normal distribution with mean 8 and variance 25. Thus the…
A: The mean is 8 and the variance is 25.
Q: Consider the continuous normal random variable, X = {a typical customer’s expenditure at Baby-Toy…
A: Draw the normal curve and shade the area to the left of z=-1. Refer to Standard normal…
Q: A small ferry runs every half hour from one side of a large river to the other. The number of cars X…
A: The objective of the question is to define the random variable M, which represents the money…
Q: Costs for standard veterinary services at a local animal hospital follow a Normal distribution with…
A: GIVEN DATA normal distributionμ = 89σ = 23P(45<x<132) = ?
Q: A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean…
A:
Q: For a random variable X with standard deviation 5, Variance of 2x + 4 is Question 4Select one: a.…
A: Answer is in the explanation box.Explanation:
Q: A random sample of size 40 was drawn from a normal distribution with the mean 50 and standard…
A:
Q: Given the standard normal random variable Z, find Pr(-2.08 <ZS 1.76). O A. 0.9420 O B. 0.0580 O C.…
A: We need to compute Pr(−2.08≤Z≤1.76), where Z has a standard normal distribution.
Q: Glaucoma is a disease of the eye that is manifested by high intraocular pressure. The distribution…
A: The mean (µ) is 15 mm Hg.The variance is 9 mm Hg.The standard deviation is square root of the…
Q: On average, Americans spent $940 dollars on holiday gifts in 2019, with a standard deviation of…
A: Here, we have given that on average , Americans spent $ 940 dollars on holiday gifts in 2019, with…
Q: The average cost per household of owning a brand new car is $5000. Suppose that we randomly selected…
A: Z-score formula : z = (x̄ - μₓ̄ )/σₓ̄
Q: The World Health Organization's (W.H.O.) recommended daily minimum of calories is 2600 per…
A: given data W.H.O. minimum calories = 2600 μ = 2460σ = 500n = 49P(x¯ >2600) = ?
Q: Given independent random variables with means and standard deviations as shown, Mean SD X…
A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to…
Q: Given that z is a standard normal random variable, what is the probability that -2.51 SS-1.532…
A: Given Data: z represents the standard normal distribution To Find: P(-2.51<z<-1.53)
Q: If ?(−2 < ? < ?) = .6, where Z is a standard normal random variable, what is the value of ??
A: Correct answer is 0.313
Q: A man height and weight are nomally distributed with mean u= 70 inches and standard deviation a =…
A:
Q: Suppose that Z is a normal random variable. Fine P(Z>1.91).
A: Solution:- from given information Suppose that Z is a normal random variable
Q: Suppose the random variable X follows a normal distribution with mean 8 and variance 25. Thus the…
A: Given, Mean μ = 8Variance σ2 = 25Standard deviation σ = Variance = 25 = 5
Q: occurs? (d) If a car accident has not happened in 3 hours, what is the probability it will happen in…
A: One car accident in 60 mile road occuring in 60 minutes . Car accidents are independent Two…
Q: Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took…
A: a. The level of significance is 0.05. Null hypothesis: H0:µ=85. Alternative hypothesis: H1:µ>85.…
Q: Given that Z is a standard normal random variable, what is the value of Z if the area to the left of…
A: The random variable Z follows standard normal distribution. We have to find the value of Z if the…
Q: f z
A: As, z is a standard number variable, so Mean (μ) = 0 Standard Deviation (σ) = 1 So, Z = z-01~N(0,1)
Q: Consider the continuous normal random variable, X = {a typical customer’s expenditure at Baby-Toy…
A:
Q: Given that z is a standard normal random variable, what is the value of the z score (a) if P (z >…
A: We want to find a such that P(z≥a) = 0.1949
Q: The distribution of the amount of water used per wash cycle, in gallons, by a particular brand of…
A: Given information Mean (µ) = 4 Gallons Standard Deviation (σ) = 0.2 Gallon Probability that more…
Q: The random variable ?, which is the number of telephones coming to a telephone exchange in a…
A: Part (a) Let X be a random variable denotes the number of telephone calls coming to a telephone…
Q: For a normally distributed random variable, the population mean is 4.32 and population standard…
A:
Q: What is the most that a male penguin can weigh to be considered a chick? Given that a male penguin…
A: Given The distribution of weights of male penguin is assumed to be normal with a population…
Q: In a certain state, the daily amounts of industrial waste are normally distributed with a mean of…
A: Let us denote X=the daily amounts of industrial wasteGiven that X is normally distributed with…
Q: According to a recent study, students at land-grant universities spend between $650 and $950 per…
A: Given : The students at land - grant universities spend between $650 and $950 per year on…
Q: An automated machine in a manufacturing process is operating properly if the length of animportant…
A:
Q: Find a value of the standard normal random variable z, called zo, such that P(z < zo) = .43 O A. Zo…
A: Let Z be the random variable from standard normal distribution with mean = 0 and standard deviation…
Q: The compressive strength of samples of cement can be modeled by a normal distribution with a mean of…
A: Given, Mean = 6000 Standard deviation = 100 The objective is to find the probability that the…
Q: 11. Assume that the weights of individuals are independent and normally distributed with a mean of…
A: Given data Assume that the weights of individuals are independent with mean of 160 and standard…
Q: Suppose A and B are two events. If P(A)=0.5, P(B)=0.4, and P(AUB)=D0.8. Then find the P(ANB)?
A: Note : Since you have asked multiple questions, we will solve the first question for you. If you…
Q: obability of a boy =0.5. Finc obability of less than 2 boys- ormal approximate probabilit boys. DA.…
A: Given n=10 P=0.5
A paint manufacturer produces cans of paint of nominal volume 2 litres.
In fact the volume of paint in a can is a Normal random variable with
A single can is examined; the probability that it contains less than 2 litres is (3 d.p.)?
Step by step
Solved in 2 steps with 1 images
- A machine produces glass with a nominal thickness of 4mm. In fact the thickness is a Normal random variable with mean 4.168mm and standard deviation 0.12mm. The thickness in mm which 5% of panes exceed is (2 d.p.)?Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 94 87 83 104 98 108 84 89 The sample mean is x = 93.4. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that o = 12.5. The mean glucose level for horses should be u = 85 mg/100 ml.t Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 85; H,: u + 85; two-tailed O Ho: H = 85; H: µ > 85; right-tailed O Ho: H > 85; H,: µ = 85; right-tailed O Ho: H = 85; H,: µ < 85; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume…The average cost per household of owning a brand new car is $5,500. Suppose that we randomly selected 45 households, determine the probability that the sample mean for these 45 households is between $5,250 and 6,000. Assume that the variable is normally distributed and the standard deviation is $1,550. SD of the sample mean (input 4 decimal places)= type your answer... type your answer... z-scores (input 2 decimal places) type your answer... Final answer/Probability (input 2 decimal places type your answer... %
- In a study of life expectancy in a certain region, the mean age at death was 70 years, and the standard deviation was 5 years. The life expectancy (years) is assumed to follow a skewed distribution. Suppose that a random sample of 45 people from this region is selected. The mean life expectancy (years) of the sample is considered a random variable. What is its standard error? 0.5976 O 2.2361 O 5.2341 O 0.1111MN.27.Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.7054? A.-0.54 B.1.54 C.0.54 D.-1.54
- Coal is carried from a mine in west virginia to a power plant in new york in hopper cars on a long train. The automatic hopper car loader is set to put 77 tons of coal into each car. The actual weights of coal loaded into each care are normally distributed with mean u= 77 tons and standard deviation 0= 1.1 ton. A. What is the probability that one car chosen at random will have less than 76.5 tons of coal? ( Round your answer to four decimal places.) B. What is the probability that 29 cars chosen at random will have a mean load weight x of less than 76.5 tons of coal? ( Round your answer to four decimal places) C. Suppose the weight of coal in one car was less than 76.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment. Suppose the weight of coal in 29 cars selected at random had an average x of less than 76.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?The general philosophy of standardizing is that standardizing a random variable involves a. Subtracting the main in the batting by the standard deviation b. Dividing the standard deviation of the total of successes by the total of trials c. Adding and subtracting standard deviations in each direction d. Subtracting the area in the right tail from 1 since the Z chart gives only the area "to the left"The mean height of 15-year-old boys (in cm) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. Assuming that the two populations are normally distributed. If eight boys and eight girls were sampled, then the probability that the mean height of the sample of boys will exceed the mean height of the sample of girls by 1 or more is: O 0.9938 0.9878 0.0062 O 0.9972
- The distribution of weekly salaries at a large company has a mean of $1000 and a standard deviation of $350. What is the probability that the mean of a random sample of weekly salaries of 50 employees will be at most $900? 0.0217 O 0.9783 O 0.3438 O Cannot be determined, because the distribution of the population is not normal.Two normally distributed populations with H4 =µ, and both variances being 100 are given. Random samples of size 25 are taken from each population with respective sample means 104 and 100. What is the probability of observing a difference of at least 4 units between the first and second sample means? Select one: O a.None b.0.1271 c.0.8729 d.0.9207 e.0.0793Indrilling a vertical wellbore, the spacing between major fractures are recorded. It has been found that this spacing is having a mean of 180o ft and a variance of 3,240,000 ft In the first 2000 ft drilling, there was no present of major fracture in the well. Determine the probability that there is a major fracture at the depth of 2000-3500 ft. Select one: a.0.57 b.o.43 C. O.19 do 82
