1/19/17 2:56 PM Homework: Lesson 5, Section 5.2 Homework yStat Save Score: 0 of

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1/19/17 2:56 PM Homework: Lesson 5, Section 5.2 Homework yStat Save Score: 0 of 1 pt My C 60f 8 (0 complete) HW Score: 0%, 0 of 8 pts Cours 5.2.12 Question Help The times per week a student l selected. Find the following probabilities. uses a lab computer are normally distributed, with a mean of 6.4 hours and a standard deviation of 1.4 hours. A student is randomly Home that the student uses a lab computer less than 4 hours per week (b) Find the probability that the student uses a lab computer between 6 and 8 hours per week t uses a lab computer more than 9 hours per week. Grade (a) The probablity that a student uses a lab computer less than 4 hours per week is StatC Chapt Tools t Multim Purc Pears Discu Coursiremaining Syllabus (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. Clear All Check Answer 19

Explanation / Answer

X : Usage time per week of lab computer by students

X follows normal distribution with mean 6.4 and standard deviation 1.4

(a) Probability that the student uses a lab computer less than 4 hours per week = P(X<4)

P(X<4)

Z-score for 4 = (4-mean)/Standard Deviation = (4-6.4)/1.4 = -2.4/1.4 = -1.71

from standard normal tables , P(Z< -1.71) = 0.0436

P(X<4) = P(Z< -1.71) = 0.0436

Probability that the student uses a lab computer less than 4 hours per week = P(X<4) = 0.0436

(b) Probability that the student uses a lab computer between 6 and 8 hours per week = P(6<X<8) = P(X<8) - P(X<6)

P(X<8)

Z-score for 8 = (8-6.4)/1.4 = 1.6/1.4 = 1.14

From standard normal tables P(Z<1.14) = 0.8729

P(X<8) = 0.8729

P(X<6)

Z-Score for 6 = (6-6.4)/1.4 = -0.4/1.4 = -0.29

From standrard normal tables, P(Z<-0.29) = 0.3859

P(X<6) = 0.3859

P(6<X<8) = P(X<8) -P(X<6) = 0.8729 - 0.3859 = 0.487

Probability that the student uses a lab computer between 6 and 8 hours per week = 0.487

(c) Probability that the student uses a lab computer more than 9 hours per week =P(X>9) = 1-P(X<9)

P(X<9)

Z-score = (9-6.4)/1.4 = 2.6/1.4 = 1.86

From standard tabels, P(Z<1.86) = 0.9686

P(X<9) = P(Z<1.86) = 0.9686

P(X>9) = 1-P(X<9) = 1-0.9686=0.0314

Probability that the student uses a lab computer more than 9 hours per week = 0.0314

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