A confidence interval estimate is desired for the gain in a circuit on a semiconductor device. Assume that gain is normally distributed with = 20. Find a 95% Cl for µ whenn = 10 and x = standard deviation 1000. Show critical z values calculation.

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 38 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? (i) Alpha (Enter an exact number as an integer, fraction, or decimal.)? =

Suppose that X follows a lognormal distribution with w^2=4 and E(X)=10,000 a. Find the parameter theta for the distribution. Use 4 digits after the decimal point: b. Find the standard deviation of the process: Use 4 digits after the decimal point:

A critical communications relay has a constant failure rate of 0.1 per day. Once it has failed, the mean time to repair is 2.5 days (the repair rate is constant). Calculate the interval availability over a 2-day mission (starting at time zero) and the point availability at the end of the 2 days.

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken six blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.83 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) lower limit= upper limit= margin of error=   (d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.02 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)

In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 9090 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000150,000 miles of driving) of the vehicle. NOX ++ NMOG emissions over the useful life for one car model vary Normally with mean 8484 mg/mi and standard deviation 66 mg/mi. (a) What is the probability that a single car of this model emits more than 9090 mg/mi of NOX ++ NMOG? (Enter your answer rounded to four decimal places.) (b) A company has 1616 cars of this model in its fleet. What is the probability that the average NOX ++ NMOG level ?¯x¯ of these cars is above 9090 mg/mi? (Enter your answer rounded to four decimal places.)

A certain variable has a bell-shaped distribution with mean μ=176.16μ=176.16 and standard deviation σ=4.9σ=4.9. You observe a value of x=184x=184. Is this a TYPICAL value of the variable (within 2 standard deviations of the mean), or an UNUSUAL one (more than 2 standard deviations from the mean)?