Assignment:
If Z is a standard normal variable, find the probability.
1)The probability that Z is less than 1.13
2)The probability that Z is greater than -1.82
3)P(-0.73 < Z < 2.27)
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 degrees C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0 degrees C (denoted by negative numbers) and some give readings above 0 degrees C (denoted by positive numbers). Assume that the mean reading is 0 degrees C and the standard deviation of the readings is 1.00 degrees C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information.
4)If 7% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.
Find the indicated probability.
5)The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?
Solve the problem.
6)Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 63.2 inches and 64.0 inches.
Use the confidence level and sample data to find a confidence interval for estimating the population μ.
7)A group of 51 randomly selected students have a mean score of 25.4 with a standard deviation of 3.1 on a placement test. What is the 90 percent confidence interval for the mean score, μ, of all students taking the test?
8)A random sample of 144 full-grown lobsters had a mean weight of 18 ounces and a standard deviation of 2.9 ounces. Construct a 98 percent confidence interval for the population mean μ.
Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ.
9)Margin of error: $ 126, confidence level: 99%, σ = $ 534
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.
10)A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 193 milligrams with s = 15.4 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content of all such eggs.