Learning Materials
Features
Discover
Chapter 6: Q. 106 (page 431)
Large Counts condition To use a Normal distribution to approximate binomial probabilities, why do we require that both and be a t least ?
the shape of binomial distribution to normal distribution n p and n p 10 is used.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Benford鈥檚 law Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren鈥檛 present in legitimate records. Some patterns, like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford鈥檚 law. 4 Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit cannot be 0).
Part (a.) A histogram of the probability distribution is shown. Describe its shape.
Part (b). Calculate and interpret the expected value of X.
Electronic circuit The design of an electronic circuit for a toaster calls for a ohm resistor and a -ohm resistor connected in series so that their resistances add. The components used are not perfectly uniform, so that the actual resistances vary independently according to Normal distributions. The resistance of -ohm resistors has mean ohms and standard deviation ohms, while that of -ohm resistors has mean 250 ohms and standard deviation 2.8ohms.
(a) What is the distribution of the total resistance of the two components in series?
(b) What is the probability that the total resistance
Easy-start mower? A company has developed an "easy-start" mower that cranks the engine with the push of a button. The company claims that the probability the mower will start on any push of the button is 0.9. Assume for now that this claim is true. On the next 30 uses of the mower, let the number of times it starts on the first push of the button. Here is a histogram of the probability distribution of T :
a. What probability distribution does T have? Justify your answer.
b. Describe the shape of the probability distribution.
Lie detectors A federal report finds that lie detector tests given to truthful persons have probability 0.2 of suggesting that the person is deceptive. 11 A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let Y= the number of people whom the lie detector indicates are being deceptive.
a. Find the probability that the lie detector indicates that at least 10 of the people are being honest.
b. Calculate and interpret .
c. Calculate and interpret .
Toothpaste Ken is traveling for his business. He has a new -ounce tube of toothpaste that鈥檚 supposed to last him the whole trip. The amount of toothpaste Ken squeezes out of the tube each time he brushes is independent, and can be modeled by a Normal distribution with mean ounce and standard deviation ounce. If Ken brushes his teeth six times on a randomly selected trip, what鈥檚 the probability that he鈥檒l use all the toothpaste in the tube?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine