The mean of the commute time to work for a resident of a certain city is 27.8 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to complete parts (a) through (c). (a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the mean? % (Type an integer or a decimal.) (b) What minimum percentage of commuters in the city has a commute time within 2.5 standard deviations of the mean? What are the commute times within 2.5 standard deviations of the mean? The minimum percentage of commuters in the city that has a commute time within 2.5 standard deviations of the mean is %. (Round to one decimal place as needed.) The commute times within 2.5 standard deviations of the mean are between and (Type an integer or a decimal. Use ascending order.) (c) What is the minimum percentage of commuters who have commute times between 3.5 minutes and 52.1 minutes? |% (Round to one decimal place as needed.)

Q: An investigator is interested in the possibility of merging the capabilities of television and the…

A: 1] n=50 2] μ=11.5 3] s=3.5

Q: The lifespan of lightbulbs is normally distributed with a mean of 300 days and standard deviation of…

A: From the provided information, Mean (µ) = 300 days Standard deviation (σ) = 50 days Let X be a…

Q: The breaking strengths of cables produced by a certain manufacturer have a mean,  μ , of  1850…

A:

Q: A researcher claims that some particular bacteria with an average life span of 10 hours will live to…

A: Given Information: Sample size n=32 Sample mean x¯=14 Standard deviation s=4.2 Hypothesized value of…

Q: The percent of fat calories that a person in America consumes each day is normally distributed with…

A:

Q: It is believed that the mean age of all coyotes living in the wild is 1.75 years. A study involved…

A: We have to test that if mean age of coyotes is more than 1.75years.

Q: The weight of oranges growing in an orchard is normally distributed with a mean weight of 5.5 oz.…

A:

Q: breaking strengths of cables produced by a certain manufacturer have a mean, μ , of 1925 pounds, and…

A: In this case, a test is required to see whether the manufacturing process has increased the mean…

Q: Suppose that a highly selective college desires to admit students based on their performance on an…

A: Given information- Population mean, µ = 1000 Population standard deviation, σ = 200 Let, X be the…

Q: The breaking strengths of cables produced by a certain manufacturer have a mean, µ, of 1825 pounds,…

A:

Q: If a wildlife service wishes to estimate the mean number of days of hunting per hunter for all…

A: Following information is given. Confidence level is 96% Error bound = 2 population standard…

Q: Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of…

A: Solution

Q: Suppose that salaries for recent graduates of one university have a mean of $24,900 with a standard…

A:

Q: Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of…

A:

Q: 2) The manufacturer of a certain brand of automobiles component claims that mean life of these…

A:

Q: Suppose that grade point averages of undergraduate students at one university have a bell-shaped…

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

Q: he blood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.8…

A: Given data,Mean μ=253.8sd    σ=61.7P(68.7<X<438.9)=?

Q: A person must score in the upper 0.15% of admission test scores in order to qualify for a very…

A: A person must score in the upper 0.15% of admission test scores in order to qualify for a very…

Q: Determine the percent of callers who are on hold for more than 4.8 minutes.

A: Assume the hold time of callers to a cable company is normally distributed with a mean of 4.8…

Q: The average grade of second year Business Management students in a certain college is normally…

A: Given: X¯=84, σ=5, α=0.10 Formula for interval is, Interval=X¯± Zασ From the statistical table…

Q: A particular manufacturing design requires a shaft with a diameter of 23.000 mm, but shafts with…

A: From the Standard normal table, the value of z for the area to the right of 1% is 2.326.

Q: The mean number of hours for persons watching a tv show was 2.98 hours each day with a standard…

A: Given : Claim : The population standard deviation of tv watching time for teenagers is less than…

Q: Assume the annual day care cost per child is normally distributed with a mean of $6000 and a…

A: Let, X=annual daycare cost per child Given that X is normally distributed with mean= 6000 and…

Q: Suppose that grade point averages of undergraduate students at one university have a bell-shaped…

A: Solution let X: grade point of undergraduate students with a mean of 2.61 and a standard deviation…

Q: A quality-assurance inspector periodically examines the output of a machine to determine whether it…

A: We have given that  mu=2.000 , s= 0.070 , xbar= 2.025 And n=35

Q: Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of…

A: Let X, be the random variable of hemoglobin levels among healthy females (in gm/dL) is follows…

Q: Assume that infants begin crawling at an average age of 8.8 months with a standard deviation of 1.4…

A:

Q: What is the greatest amount of time that a newborn can sleep and still be in the bottom 75% of…

A: Let , X→N(μ=15.5 , σ=1.6) Our aim is to find the greatest amount of time that a newborn can sleep…

Q: Assume the hold time of callers to a cable company is normally distributed with a mean of 5.2…

A: Given that.   X~N( μ , ?^2 )   μ=5.2    , ?=0.9   Z-score =( x - μ )/?

Q: To test the hypothesis that adult women are getting less than the recommended dietary allowance of…

A: Given information Sample mean = 16.2 mg Hypothesized mean = 18 mg Population standard deviation(σ)…

Q: 8. The mean life time of sample of 100 light bulbs produced by a company is computed to be 1570…

A:

Q: Suppose that the amount of time per day that American adults spend on their mobile devices is…

A: The following information has been given: The population mean is μ=229. The population standard…

Q: In a normal distribution of wait times for roller coaster ride, the average wait time was 45 mins…

A: Given Information: Mean wait time (u) = 45 minutes Standard Deviation (s) = 12.2 minutes

Q: Suppose that the blood pressure of the human inhabitants of a certain Pacific island is distributed…

A:

Q: Suppose that a researcher is interested in estimating the mean systolic blood pressure,  μ , of…

A:

Q: Consider a University with 10000 students whose weights are normally distributed with mean of 72Kgs…

A: We want to find the number of students have weights above 80kgs , and also find the percentage of…

Q: The breaking strengths of cables produced by a certain manufacturer have a mean, μ, of 1925 pounds,…

A: Hypotheses: Denote μ as the true mean breaking strength (pounds) of cables produced after…

Q: Suppose a survey of a random sample of 100 smokers, conducted by the Department of Health, suggests…

A:

Q: The breaking strengths of cables produced by a certain manufacturer have a mean, µ, of 1875 pounds,…

A: (a)   State the hypotheses.

Q: The mean airfare for flights departing from Buffalo Niagara International Airport during the first…

A: Obtain the probability the sample mean will be within $20 of the population mean cost per flight.…

Q: Suppose the average monthly welfare (TANF) payment is $376 and the standard deviation is $40. Using…

A: 1.Chebyshev's rule:Rule 1: If k = 2, at least 75% of the data lie within 2 standard deviations to…

Q: A fiber spinning process currently produces a fiber whose strength is normally distributed with a…

A: Given: Population mean strength μ=75Pa Minimum acceptable strength = 65Pa 10% of the fiber fails to…

Q: Suppose that the creatine kinase levels among healthy males are normally distributed with a standard…

A: From the provided information, Standard deviation (σ) = 22 Let mean creatine kinase level in healthy…

Q: Suppose that a company makes light bulbs with a mean life of 310 hours, and a standard deviation of…

A: Given that, Mean, mu= 310 And standard deviation, sigma= 47 We know that, Z Score= (X-mu)/sigma

Q: The breaking strengths of cables produced by a certain manufacturer have a mean,  μ , of  1850…

A: Given data: Population mean of breaking strength of cables = 1850 pounds. Population standard…

Q: percentage of vehicles with the following speeds on this section of I-95: greater than 75 mph. Use…

A: here given  Suppose that on a certain section of I-95, with a posted speed limit of 65 miles per…

Q: Assume that the weekly sales revenue (in thousand pesos) of major markets is normally distributed…

A: i) Given information: μ=172σ=30 The percentage of such revenues between 190 and 220 is,…

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!