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The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 72 and standard deviation 3. A USE SALT (a) If a specimen is acceptable only if its hardness is between 71 and 76, what is the probability that a randomly chosen specimen has an acceptable hardness? (Round your answer to four decimal places.) (b) If the acceptable range of hardness is (72-c, 72+ c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to two decimal places.) (c) If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (Round your answer to two decimal places.) specimens

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 72 and standard deviation 3. A USE SALT (a) If a specimen is acceptable only if its hardness is between 71 and 76, what is the probability that a randomly chosen specimen has an acceptable hardness? (Round your answer to four decimal places.) (b) If the acceptable range of hardness is (72-c, 72+ c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to two decimal places.) (c) If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (Round your answer to two decimal places.) specimens

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 72 and standard deviation 3. LAUSE SALT (a) If a specimen is acceptable only if its hardness is between 71 and 76, what is the probability that a randomly chosen specimen has an acceptable hardness? (Round your answer to four decimal places.) (b) If the acceptable range of hardness is (72-c, 72 + c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to two decimal places.) (c) If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (Round your answer to two decimal places) specimens (d) What is the probability that at most eight of ten independently selected specimens have a hardness of less than 74.527 [Hint: Y= the number among the ten specimens with hardness less than 74.52 is a binomial variable; what is p?] (Round your answer to three decimal places.)
Transcribed Image Text:The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 72 and standard deviation 3. LAUSE SALT (a) If a specimen is acceptable only if its hardness is between 71 and 76, what is the probability that a randomly chosen specimen has an acceptable hardness? (Round your answer to four decimal places.) (b) If the acceptable range of hardness is (72-c, 72 + c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to two decimal places.) (c) If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (Round your answer to two decimal places) specimens (d) What is the probability that at most eight of ten independently selected specimens have a hardness of less than 74.527 [Hint: Y= the number among the ten specimens with hardness less than 74.52 is a binomial variable; what is p?] (Round your answer to three decimal places.)
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