ASTA 509 Exam 2 (Montgomery Ch. 4, 6-7.2) Sample Questions For the exam, you wil
ID: 3063569 • Letter: A
Question
ASTA 509 Exam 2 (Montgomery Ch. 4, 6-7.2) Sample Questions For the exam, you will be allowed two sides of a 3 x5 card (anything you want on it), your calculator, and the tables at the back of the text Using the following uniform density curve, answer the question. The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°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°C (denoted by negative numbers) and some give readin gs above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°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. 1) What is the probability that the random variable has a value greater than 3 Answer: 0.625 2) What is the probability that the random variable has a value between 0.1 and 0.8? Answer: 0.088 5) Find the 96th percentile (that is, the value below which 96% of the readings fall. Answer: 1.75 If Z is a standard normal variable, find the probability 3) The probability that Z is less than 1.13 A certain brand of light bulbs has a lifetime that is exponentially distributed with a mean life of 1200 hours. Answer: 0.8708 6) A room is lit by only two of these bulbs Provide an appropriate response. installed at the same time. Find the probability that there is light in the room after 1500 hours 4) Consider the uniform distribution shown below. Find the probability that x is greater than 6. Discuss the relationship between area under a density curve and probability Answer: 1-(1-e(-1500/1200)*2-4909 Find the indicated probability 0.125 7) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? Answer: 2.28% Answer: The area under the curve from 6 to 10 is thus the probability that x is greater than 6 is 0.5. Solve the problem. 8) Scores on a test have a mean of 68 and Q3 is 85. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest Answer 25.4Explanation / Answer
Solution1:
P(X>3)
=P(X+4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)
=0.125+0.125+0.125+0.125+0.125
=0.625