3.1) Researchers observed 50 random people brush their teeth and recorded the number of seconds each person spent brushi

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3.1) Researchers observed 50 random people brushtheir teeth and recorded the number of seconds each person spentbrushing. From the sample, they found a mean time of 48.4 seconds.Further, their calculations revealed that this estimate is within amargin of error of 1.15 from the true average time that all peoplespend brushing their teeth. Write the interval estimate that willestimate the true average time that people spend brushing theirteeth.
Write your answer in interval notation:( ___ , ___ )
Write your answer using inequality notation: ___ < μ < ___
3.2) The city wishes to estimate the average commutedistance for all city employees. They collect a random sample of 90employees and find a sample mean of ¯x=5.2 miles. Theyalso assume a population standard deviation of σ=1. miles. Calculate the z interval to estimate, μ , theaverage commute distance for all city employees with 95%confidence.
Round your answers to 2 decimal places.
Find the Critical Value z*: ____
Point Estimate: ___Margin of Error: ___
Write the interval as (lower bound, upper bound)( ___ , ___ )
3.3) You measure 38 backpacks' weights, and find theyhave a mean weight of 77 ounces. Assume the population standarddeviation is 10.7 ounces. Based on this, construct a 99% confidenceinterval for the true population mean backpack weight. (Note youwill use the z distribution for your critical value since thepopulation standard deviation is given.)
Write your answer in the form of point estimate ±margin oferror. Give your answers as decimals, to two places. ____ ± ____ ounces
Write your answer using inequality notation. ___ < μ <____
3.4) You work for a company that produceselectronics with integrated circuits. One of your products iscalled a "shift register." This product is designed toautomatically shut down if its operating temperature exceeds 175degrees Celsius. The manufacturing process has been designedto have a standard deviation of σ=0.4 degrees Celsius. You test a random sample 16 shift registers, and you recordthe following shut-down temperatures. Construct a 95% confidenceinterval for the overall mean shutdown-temperature.
175.87 174.87 175.05 174.98 174.04 174.78175.53 175.28 175.28 175.25 175.56 175.09175.64 174.85 174.86 174.43
(Checksum: 2801.36)
a) Find the critical value and σ¯x .
Critical Value: ___σ¯x: ____
b) Find the confidence interval: (___ ,___)