Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this​ information, answer the following questions.   ​(a) What proportion of light bulbs will last more than 62 ​hours? ​(b) What proportion of light bulbs will last 52 hours or​ less? ​(c) What proportion of light bulbs will last between 59 and 62 ​hours? ​(d) What is the probability that a randomly selected light bulb lasts less than 45 ​hours?

Q: Medical research has concluded that people experience a common cold roughly two times per year.…

A: The mean of the normal distribution, The standard deviation of the distribution,

Q: The monthly utility bills in a city are normally​ distributed, with a mean of ​$100 and a standard…

A: We want to find given probability for given questions

Q: A Texas Instrument calculator operating life is normally distributed with a mean of 3,850 hours, and…

A: Given information- Population mean, μ = 3850 hours Population standard deviation, σ = 350 hours…

Q: The fares received by Uber Drivers working in the City line are normally distributed with a mean of…

A: Let X be a continuous random variable of fares received by Uber Drivers working in the City line are…

Q: The monthly utility bills in a city are normally​ distributed, with a mean of $100 and a standard…

A:

Q: The monthly utility bills in a city are normally​ distributed, with a mean of ​$100 and a standard…

A:

Q: e monthly utility bills in a city are normally​ distributed, with a mean of ​$100   and a standard…

A: Given: Mean, μ=100 Standard deviation, σ=15 (a)  Probability that a randomly selected utility bill…

Q: A sample of 235 students was taken for an exploratory study. Each member of a random 35 of these…

A: Since the sample size is sufficiently large, and the population standard deviation is known, the…

Q: The lengths of lumber a machine cuts are normally distributed, with a mean of 96 inches and a…

A: Given,Mean, μ = 96 inches.Standard deviation, σ = 0.5 inch.Let X be a random variable represents the…

Q: A particular fruit's weights are normally distributed, with a mean of 557 grams and a standard…

A: From the given information, let X be the fruit’s weights. Here, X follows normally distribution with…

Q: A veterinary researcher takes an SRS of 60 horses presenting with colic whose average age is 12…

A: Option b is the correct answer.

Q: builtrite has calculated average weekly daily sales to be 80000 with a standard deviation of 12000.…

A: Mean()=80000standard deviation()=12000 one store manager made a bet with another store manager that…

Q: Suppose the weight of an adult male Labrador is normally distributed with u=71.2 pounds and a…

A: Mean()=71.2standard deviation()=3.4

Q: In a study of work patterns, data from 669 subjects were collected. For the time spent in child…

A: We have given that,  Let X be the random variable from normal distribution with mean (μ) = 23.08,…

Q: A company is considering drilling four oil wells. The probability of success for each well is 0.45,…

A: Solution: Let X be the number of success in  drilling  oil wells.  The probability of  success for…

Q: The monthly utility bills in a city are normally​ distributed, with a mean of ​$100 and a standard…

A: Provided information is ; Let X be the monthly utility bill mean(μ) = 100 standard deviation(σ)=15…

Q: The starting salaries of individuals with an MBA degree are normally distributed with a mean of…

A: According to the given information in this question We need to find the probability that MBA degree…

Q: The annual income for a sample of 450 part-time students is normally distributed with a mean income…

A: Given that.   X~N( μ , ?)   μ=31000 , ?=3000   Z-score =( x - μ )/?

Q: he monthly utility bills in a city are normally​ distributed, with a mean of $100 and a standard…

A: Let X be the monthly utility bills in a city are normally distributed with mean μ=$100 and standard…

Q: the life of a certain brand of car stereo is normally distributed with a mean of 5.2 years and a…

A: According to the given information in this question, we need to find the following probability

Q: A company produces light bulbs whose life follows a normal distribution, with mean (1355) hours and…

A:

Q: The monthly utility bills in a city are normally​ distributed, with a mean of ​$100 and a standard…

A:

Q: fertility rate is the number of births per 1000 women aged 15-44. The mean fertility rate of the 50…

A: According to the given information in this question We need to find the following probability

Q: Data from the Bureau of Labor Statistics’ Consumer Expenditure Survey show that annual expenditures…

A: Given information- For the year 2001- Population mean, µ = $235 Population standard deviation, σ =…

Q: A study indicates that 18- to 24- year olds spend a mean of 120 minutes watching video on their…

A: The mean is 120 minutes and the standard deviation is 20 minutes.

Q: The monthly utility bills in a city are normally​ distributed, with a mean of $100 and a standard…

A: (a) Let x be the monthly utility bills in a city which follows normal distribution with mean 100,…

Q: Assume the credit card balances of younger college educated employed persons are normally…

A:

Q: A major application of analytics in marketing is determining customer retention. Suppose that the…

A: Given, The customer leaving for another carrier from one month to the next is 0.07We have to find…

Q: The monthly utility bills in a city are normally​ distributed, with a mean of $100 and a standard…

A: X follows a Normal distribution with mean = 100 and S.D = 13 Then z=(x-mean)/SD = (x-100)/13…

Q: The heights of strawberry plants are Normally distributed with a mean of 12 inches and a standard…

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: The monthly utility bills in a city are normally​ distributed, with a mean of $100 and a standard…

A:

Q: ortion of firms will earn a return between 4% and 8%? B   To the nearest percent find the…

A: given: mean (μ)= 7.5 standard deviation(σ)=2.5

Q: What is the probability that a randomly selected student will drink less than the suggested amount…

A:

Q: A report claimed that children between the ages of 2 and 5 watch an average of 25 hours of…

A: Given, Mean = 25 Standard deviation = 3 Sample size = 40   The objective is to find the probability…

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!