A random sample X₁, X2, X3, ..., X100 is given from a distribution with known varianc Var (X₂) = 81. For the observed sample, the sample mean is X = 50.1. a. What is the variance of X? Var(X) = Find an approximate 95% confidence interval for 0 = Confidence Interval= EXį.

Arsenic blood concentrations in healthy people are Normally distributed with meanµ = 3.2 µg/dl and standard deviation o = 1.5 µg/dl. Some areas are known to have naturally elevated concentrations of arsenic in the ground and water supplies. (a) We seek proof against the claim that u = 3.2. If the claim is true, what is the sampling distribution of the mean blood arsenic concentration x in many samples of 25 adults? (N(_,_).) Sketch the density curve of this distribution. (Sketch a Normal curve, then mark the axis using what you know about finding the mean and standard deviation on a Normal curve.) (b) Assume the first sample's data gives x = 3.35 ug/dl. Mark this point on the axis of your sketch. Assume the second sample gives x = 3.75 µg/dl. Mark this point on your sketch. (c) The sample mean x = the right tail of the curve when the sample mean x lies far out towards lies close to the centre. If the population mean is µ, finding a value similar would not be too surprising, but x = is…

A cell phone manufacturer has hired you to estimate the population mean of the battery lifetimes for all phones of their latest model. You decide to measure battery lifetime by recording the time it takes for the battery charge to run out while a tester is streaming videos on the phones continuously. Then you select a random sample of 45 cell phones of the manufacturer's latest model and record their battery lifetimes. Assume that the population standard deviation of the battery lifetimes for that cell phone model (using your method of measurement) is 2.42 hours. Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 45 phones of the manufacturer's latest model. Take Sample Sample size: Number of phones Point estimate: 45 Sample mean Standard…

The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16. Determine the interval of 95% confidence for the average heights of the population. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be less than 2 cm from the sample mean?