Assume that the results are normally distributed.An experiment consists of tossing 100 dimes repeatedly and noting the number of heads each time. The graph of the number of heads turns out to be very nearly a normal curve, with a mean of 50 and a standard deviation of 5. (Enter your answers as whole numbers.)(a) Within what limits would you expect the number of heads to be 68% of the time?lower limit headsupper limit heads(b) What percent of the time would you expect the number of heads to be between 40 and 60? %(c) Suppose that a particular dime arouses your suspicion by turning up heads too often. You toss this dime 100 times. How many times will it have to turn up heads in order for you to be almost 100% certain that it is not a fair coin? (Hint: Most of the data in a normal distribution fall within 3 standard deviations of the mean.)more than times

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Answered: Within what limits would you expect the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Assume that the results are normally distributed.

An experiment consists of tossing 100 dimes repeatedly and noting the number of heads each time. The graph of the number of heads turns out to be very nearly a normal curve, with a mean of 50 and a standard deviation of 5. (Enter your answers as whole numbers.)

(a) Within what limits would you expect the number of heads to be 68% of the time?

lower limit	heads
upper limit	heads

(b) What percent of the time would you expect the number of heads to be between 40 and 60?
%

(c) Suppose that a particular dime arouses your suspicion by turning up heads too often. You toss this dime 100 times. How many times will it have to turn up heads in order for you to be almost 100% certain that it is not a fair coin? (Hint: Most of the data in a normal distribution fall within 3 standard deviations of the mean.)
more than times

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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