The lifetime, in hours, of a head gasket of a cylinder in a car engine is distributed as lognormal with parameters a = 10.328 and 3 = 1.575. - (a) Determine the mean. 105694.96120 (b) Determine the standard deviation. 349732.63296 (c) Find the probability that the lifetime of the head gasket is between 5748 and 8435 hours.

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime (in years) which follows an exponential distribution with parameter A = 1/4. Find the probability that the lifetime of his laptop battery is less than 2.5 years and that the lifetime of his tablet battery is less than 3.2 years. (Answer as a decimal number, and round to 3 decimal places).

Assume that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C. A thermometer is randomly selected and tested. Find the probability of each reading in degrees.(a) Between 0 and 1.64: (b) Between −2.89 and 0: (c) Between −1.78 and 1.03: (d) Less than −2.79: (e) Greater than 2.62:

Suppose the mean cholesterol levels of women age 45-59 is 5.2 mmol/l and the standard deviation is 0.7 mmol/l. Assume that cholesterol levels are normally distributed. Find the probability that a woman age 45-59 has a cholesterol level above 6.1 mmol/l (considered a high level). Round to four decimal places.P(x > 6.1) =  Suppose doctors decide to test the woman’s cholesterol level again and average the two values. Find the probability that this woman’s mean cholesterol level for the two tests is above 6.1 mmol/l. Round to four decimal places.P(x̄ > 6.1) =  Suppose doctors being very conservative decide to test the woman’s cholesterol level a third time and average the three values. Find the probability that this woman’s mean cholesterol level for the three tests is above 6.1 mmol/l. Round to four decimal places.P(x̄ > 6.1) =

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 156000 dollars. Assume the standard deviation is 36000 dollars.Enter each answer as a number between 0 and 1 accurate to 4 decimal places. Find the probability that salary of a randomly selcted single graduate is at least 154000 dollars.P(X > 154000) =

Suppose that the TSH (Thyroid Stimulating Hormone) levels among healthy individuals are normally distributed with a mean of 3.2 units/mL. Suppose also that exactly 98% of healthy individuals have TSH levels below 6.1units/mL. Find the standard deviation of the distribution of TSH levels of healthy individuals. Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.