I just need to know how to find this using my calculator Previous Problem Proble

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I just need to know how to find this using my calculator

Previous Problem Problem List Next Problenm (1 point) Given a normal population whose mean is 435 and whose standard deviation is 35,find each of the following A. The probability that a random sample of 4 has a mean between 438 and 447 Probability B. The probability that a random sample of 17 has a mean between 438 and 447. Probability = C. The probability that a random sample of 24 has a mean between 438 and 447 Probability = ns Note: You can earn partial credit on this problenm Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining

Explanation / Answer

From the information

mu = 435 and sigma = 35

Part A :

n= 4

Required probability = P( 438 < Xbar < 447)

Z =(Xbar - mu ) /( sigma/sqrt(n)) ~ N(0,1)

P( 438 < Xbar < 447 ) = P(( 438-435)/(35/sqrt(4) ) < Z < ( 447-435)/(35/sqrt(4)) )

= P( 0.1714 < Z < 0.6857)

= P( Z > 0.1714) - P( Z>0.6857)

From Normal Probability table

P( Z > 0.1714) =0.432 and P( Z>0.6857) = 0.2465

P( 438 < Xbar < 447 ) = 0.432 -0.2465 = 0.1855

Part B:

n= 17

Required probability = P( 438 < Xbar < 447)

Z =(Xbar - mu ) /( sigma/sqrt(n)) ~ N(0,1)

P( 438 < Xbar < 447 ) = P(( 438-435)/(35/sqrt(17) ) < Z < ( 447-435)/(35/sqrt(17)) )

= P( 0.3534 < Z < 1.4136)

= P( Z > 0.3534) - P( Z>1.4136)

From Normal Probability table

P( Z > 0.3534) =0.3619 and P( Z > 1.4136) = 0.0787

P( 438 < Xbar < 447 ) = 0.3619 -0.0787 = 0.2832

Part A :

n= 24

Required probability = P( 438 < Xbar < 447)

Z =(Xbar - mu ) /( sigma/sqrt(n)) ~ N(0,1)

P( 438 < Xbar < 447 ) = P(( 438-435)/(35/sqrt(24) ) < Z < ( 447-435)/(35/sqrt(24)) )

= P( 0.4199 < Z < 1.6796)

= P( Z > 0.4199) - P( Z >1.6796)

From Normal Probability table

P( Z > 0.4199) =0.3373 and P( Z>1.6796 = 0.0465

P( 438 < Xbar < 447 ) = 0.3373 -0.0465 = 0.2908

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