Reference no: EM13337839
A certain type of automobilebattery is being assessed for its lifetime. The productionmanager selected a random sample of batteries and gatheredinformation for them. The lifetimes in years, gathered were :{3.25, 4.0, 3.1 3.7, 3.5, 4.2, 4.75, 2.3, 2.5, 3.7}. Answer thefollowing assuming that the population is normal. (Each isworth 2 points, except part i)
a. What is the samplemean?
b. What is the samplevariance?
c. What is the samplestandard deviation?
d. Explain how the sample mean isrelated to the population mean.
e. Use the sample mean andsample standard deviation to illustrate the hypotheticaldistribution of the population. Label values at±1, ±2 and ±3 standard deviations.
f. Assume that you know thatthe standard deviation of the population is 0.710; construct a 90%confidence interval for . (Show formula)
g. Explain or interpret this lastinterval.
h. For how long should thesebatteries be guaranteed if the manufacturer wants to replace only5% of the batteries sold because they “died” before thewarranty period?
i. Determine the needed sample size if the manager wantedto have a 99% confidence interval with an error margin of 3months.
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