An archer can either hit or miss his target. The probability of hitting a target is 50.0% . Suppose, he will take 17 attempts on a specific day. a. What is the mean number of attempts in which he hits the targets? Answer in exact fraction, or rounded to at least 2 decimal places. b. What is the standard deviation in the number of successful attempts? Answer in exact fraction, or rounded to at least 2 decimal places. c. What is the probability that the number of successful attempts is more than 1 standard deviations away from the mean value? Answer in exact fraction, or rounded to at least 4 decimal places.
An archer can either hit or miss his target. The probability of hitting a target is 50.0% . Suppose, he will take 17 attempts on a specific day. a. What is the mean number of attempts in which he hits the targets? Answer in exact fraction, or rounded to at least 2 decimal places. b. What is the standard deviation in the number of successful attempts? Answer in exact fraction, or rounded to at least 2 decimal places. c. What is the probability that the number of successful attempts is more than 1 standard deviations away from the mean value? Answer in exact fraction, or rounded to at least 4 decimal places.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
![An archer can either hit or miss his target. The probability of hitting a target is 50.0% . Suppose, he will take 17 attempts on a specific day.
a. What is the mean number of attempts in which he hits the targets?
Answer in exact fraction, or rounded to at least 2 decimal places.
b. What is the standard deviation in the number of successful attempts?
Answer in exact fraction, or rounded to at least 2 decimal places.
c. What is the probability that the number of successful attempts is more than 1 standard deviations away from the mean value?
Answer in exact fraction, or rounded to at least 4 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe17fb59c-84e2-4097-95f3-98832f024a61%2Fe216af77-9ca3-4381-954f-ea265708978a%2Fdsb4a8_processed.png&w=3840&q=75)
Transcribed Image Text:An archer can either hit or miss his target. The probability of hitting a target is 50.0% . Suppose, he will take 17 attempts on a specific day.
a. What is the mean number of attempts in which he hits the targets?
Answer in exact fraction, or rounded to at least 2 decimal places.
b. What is the standard deviation in the number of successful attempts?
Answer in exact fraction, or rounded to at least 2 decimal places.
c. What is the probability that the number of successful attempts is more than 1 standard deviations away from the mean value?
Answer in exact fraction, or rounded to at least 4 decimal places.
Expert Solution
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Step 1
Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials being independent and the probability of success, say p, remaining constant, then the distribution of the number of success follows binomial.
Let us assume X be a random variable denoting the number of success.
Then , n and p being the parameters of the binomial distribution.
The probability mass function of X is given by,
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