Math 1342 Statistics Information
Task:
1. Find the area of the shaded region. The graph depicts the standard normal distribution. You can use technology and one number will be enough. Please write carefully the answer using the correct format P(XXX)=YYYY
2. Find the indicated z-score. The graph depicts the standard normal distribution. You can use the calculator and write the answer correctly as an equality (see the notes). Shaded area is 0.0901.
3. For this exercise please show the following:
a) The graph of normal distribution related with the problem information
b) Write the answer in correct form
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 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 (denoted by negative numbers) and some give readings above (denoted by positive numbers). Assume that the mean reading is and the standard deviation of the readings is 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. If 9% 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.
4. Show all the work step by step of finding the margin of error as were presented in the lecture notes. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.
99% confidence; n = 5900, x = 1770
5. For this exercise you can use the technology. Write the answer in proper way (see the notes). Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 130, x = 69; 90% confidence.
6. Show work step by step. Use the given data to find the minimum sample size required to estimate the population proportion.
a) Margin of error: 0.045; confidence level: 96%; and unknown
b) Margin of error: 0.07; confidence level: 90%; from a prior study, is estimated by 0.30.
